Real World Math Part 3 – What are Logarithms good for?

In the previous article about depreciation, we introduced the exponential depreciation model. It is an excellent tool for use in a variety of fields. However, when applied to depreciation of monetary value over time, such as our automobile example, we discovered the difficulty of working with variables when they show up as an exponent.

Guess and check put us in the ball park for determining when our example vehicle – the Toyota Corolla MSRP at \$21,000 financed over 5 years, has a value less than the cost of financing the car.

Instead of using the ball park method, there is a more elegant way to calculate a precise interval of time before our Toyota’s value is less than the finance charge. The following should give you some appreciation for why I like having logarithms available in my real world math tool kit.

First of all, logarithms are used to convert equivalent values between Log expressions and exponential expressions. For example:

Say we have an exponential expression: 1,000=10x When this expression is translated into a logarithmic expression, it it will look like this: log(1000)=3

When using the “Log” symbol on most calculators, it implies the log base is 10:

log10 1000 = 3

Our exponential decay model in the depreciating Toyota example follows:

\$21,000 x 0.8(yrs) < \$6,189 Simplified to – 0.8(yrs) < 0.2947

This inequality is still in exponential form with the variable in the exponent, so let’s convert it to logarithmic form:

log0.8(0.29) = yrs

But wait, my calculator doesn’t allow me to change the base of the logarithm from 10 to 0.8!

No worries, there is a formula for this very specific situation and it is called (would you believe?), the “change log formula.” As applied to our problem we get the following, which we can type into our calculator to get the exact amount of years:

log(0.29)/log(0.8) = 5.54 yrs

As you can see, the mathematicians of old have done a lot of hard work figuring things out for us. There are more situations where this relationship between exponential expressions and logarithmic expressions can be useful. Perhaps the most important point of this real world math exercise is the understanding that numbers, mathematical operations, ratios and formulas can be related to one another in a variety of ways. Filling your math tool kit with knowledge of these relationships can save lots of time spent wondering how to solve real world math problems.

Real World Math Part 2 – Depreciation

Previously we took a look at the down side of buying a new car with a loan. This time let’s do some further analysis using another cool formula to keep at the ready which can assist you with making purchase decisions. Works for cars, laptops, a new roof for your house, or any other thing you can buy that ages, goes obsolete or simply wears out.

We’ll use our \$21,000 MSRP Toyota Corolla to look at asset depreciation. Granted, there are several factors that play into the depreciation of a new car. Milage, age, condition, adherence to a manufacturer’s maintenance schedule etc. all factor into a cars value at a certain point in its lifespan. However, for the purpose of analyzing rate of depreciation, we’ll leave out the other factors. In fact each manufacturer uses the various quality factors to calculate a vehicle’s affordability. Some cars are built to be inexpensive to own/maintain but have short lifespans, while others have strict and expensive maintenance schedules that are geared toward reliability and a long life.

The Problem:

Leaving all the other factors out, if our \$21,000 Corolla depreciates 20% over the first year of its life, how many years would pass before the car’s value is equal to or less than the amount of interest we would have paid for the \$19,500 we financed?

• Cost of vehicle = \$21,000.
• Total interest paid on vehicle = \$6,189
• Rate of depreciation = 20% subtracted from 100% leaves 80% or a factor of 0.80 for annual depreciation.

Formula: Cost x Rate^yrs = depreciated value

\$21,000 x 0.8 (yrs)≤ \$6,189

(Figuring out the value of the exponent will give the number of years before the car’s value is equal to or less than the amount of interest we paid on the loan)

0.8 (yrs)≤ \$6,189÷\$21,000 this gives 0.8 (yrs)≤ 0.2947

To calculate the number of years, we need to guess and check by plugging in some values for the exponent. You can even bracket the values of the exponents:

0.8 2 = .64 which is bigger than our 0.2947 and we’re looking for the same or less

0.8 8 = .1677 which is smaller, so the number of years will be somewhere in between.

Let’s try an exponent of 6: 0.8 6 = 0.2621 which is less than or equal to the figure in our formula.

The answer here is that the car’s value will be less than the interest paid on the loan after 6 years. Another way to look at this is when the car loan is paid at the end of 5 years, you’ll be driving a paid for car for 1 year before it has little or no value – if you sell it for \$6,200 you’ll essentially be getting nothing since this is the money you already paid to the bank to finance it.

In part 3 of Real World math, we will look at compounding interest at rates other than annual (semi annual, quarterly, and monthly).

Real World Math – Why you should never get a car loan

As a private Math tutor, my students often ask why or when in the real world, they will ever need the math skills they’re required to develop in middle and high school. The example below seems to work and gets their attention.

So you want to buy a new car someday? Better start saving up, and here is why:

Let’s say you decide on the most practical and popular car sold in the USA, a Toyota Corolla with an MSRP around \$21,000. We all know there will be additional costs that could jack that price up by a couple thousand more, but for this example we can use the MSRP. You might think that is a lot of cash to save, so you look into a car loan.

While doing some research you learn that most dealers require a down payment. A good thing you banked \$1,500 from the lifeguarding job you had last summer between your Junior and Senior year. Plus, now that you have a regular part time job at Petco grooming poodles, you can actually qualify for a loan so long as your parents co-sign.

Since your parents agree to co-sign, the dealer offers you a killer loan – with an annual interest rate of 5.75% for 60 months. Of course the dealer wants to sell you the car based on a monthly payment and convince you to purchase additional options – “Bluetooth hands free will only cost you an addition \$8/month, you’ll also want the Navigation and color display I showed you during your test drive for another \$22/month.”

You figure since you’re financing the car anyway, what’s a couple extra bucks a month? Besides, you love the candy apple metallic red with cream faux leather interior. With mom and dad on the sidelines wishing your experience at the dealer will serve as an education you begin to wonder how much this car is actually going to cost you.

A nagging memory from 11 grade algebra comes into play because you recall there is a quick and easy way to do the calculation, but you don’t remember the formula. So in case you read this article before shopping for a car, here’s a quick review:

The exponential growth model is an excellent tool to file away in your memory. Hopefully you’ll use it so often that it will immediately come to mind anytime a credit card application arrives in the junk mail.

Base x rate with an exponent the value of the time interval. In this case you will be financing \$19,500 at 5.75%, 60 months translates to 5 years, so that will be your exponent. Your formula and result will look like this:

\$19,500 x 1.05755 = \$25,689

That doesn’t even include the down payment! Oh and the monthly payment is what now? \$418 per month? Are you going to have enough left over from your part time job to maintain your nice new car, put gas in it, be nice and offer to pay your parents the add on to their insurance policy?

Your mom and dad are pleased when you realize the car will actually cost you more than \$6000 above the price advertised. When you leave the dealership with your parents but without a new car, your dad says he’ll give you an interest free loan and help you find a safe/reliable pre-owned car for close to the amount the interest you’d have had to pay if you’d financed a new car.

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Social Security: When to Start Drawing?

Boomers are smack dab in the middle of eligible retirement age facing a decision about when to draw from Social Security. There is no such thing as a one size fits all decision tool. For example, if both partners in a marriage are at an age for drawing Social Security and one partner passes away, the surviving partner is eligible for the higher of the two original incomes.

What if you want to draw and continue to work part time? This is definitely something to think about, because there is potential for a reduction in your earned benefit you would be receiving if your income from working part time exceeds \$18,240.

What if you are a disabled veteran in receipt of a service connected monetary monthly benefit? The basic rule is a recipient isn’t allowed to double dip. In other words, the beneficiary will receive the higher of the two monthly income benefits but not both. Usually the way this works is if Social Security income exceeds the VA benefit, the veteran will only receive Social Security. If the VA benefit is higher, the beneficiary will receive Social Security and the VA will augment to make up the difference. For example if a veteran is permanently disabled at a condition rating where the veteran is receiving \$1,200/month from VA and is eligible for Social Security at \$1,050/month, the beneficiary will receive the total \$1,200/month (\$1,050 from Social Security and \$150 from VA). What if the veteran’s disability rating results in monthly income greater than the Social Security early retirement figure? That would amount to an easy decision to wait until full retirement or delayed retirement (whichever results in a figure greater than the VA benefit).

For most people, the first order of business might be to gain a clear picture of the basics. For those of us born during/after 1960, eligibility for early retirement is age 62 and full retirement is age 67. There is also a different monthly income figure for people wishing to delay drawing until age 70. One way to help analyze the decision for when to draw SSI is to determine at what age would a person be when the amount drawn from early retirement vs full retirement is the same.

Let’s say for a person born 1960 and later, the figure for drawing early from SSI is \$1,120/month. Waiting another 5 years for full retirement and drawing at age 67 would generally be 30% higher at \$1,600/month. For every year after up to age 70 (3 more years) a delay would be 108% for each year’s monthly income over age 67. e.g. delaying to age 68 your income would be \$1,728/month. For age 69 it would be \$1866/month and age 70 (maximum) would be \$2,015/month. These differences as a person ages seem to indicate some advantage for waiting for full retirement or even delaying drawing SSI until age 70, but is it really an advantage? Knowing how all the facts line up before making the decision to draw makes good sense. Using the figures above we can analyze the facts using basic algebra in the following example:

What we want to know is the number of years before the amount drawn at full retirement age of 67 is the same as the amount one would have drawn starting early at age 62.

Draw at 62: \$1,120/month = \$13,440/yr
For years 62-67 amount drawn = \$67,200
Draw at 67: \$1,600/month = \$19,200/yr

Let x = number of years before amount drawn is the same.

First 5 years:
Early = \$67,200
Full = \$0
Variables:
Full = \$19,200x + \$0
Early = \$13,440x + \$67,200
Formula:
\$13,440x + \$67,200=\$19,200x
\$67,200 = \$5,760x
\$67,200/\$5,760 = x = 11.66

The dollars cancel leaving 11.7 years, so the retiree’s age would be 78.7 years old before the amount drawn is the same. To calculate your own figures, just plug them into the template above. You can also assess the advantage or disadvantage if you delay beyond age 67.

As mentioned above, there is no one-size solution for these decisions. An individual’s health and longevity will play heavily into the equation.

What people with lots of \$ should know:

I recently read a non-fiction account titled “The Emerald Mile,” by Kevin Fedarko. Within the pages, I came across a passage about dam building in the United States. The passage was related to the Grand Canyon and the taming of waters draining the Colorado River basin. I’ll paraphrase: By 1980, 75,000 dams had been built in the United States, amounting to 1 for every 48 hours since the Spanish explorer Cardenas first saw the Grand Canyon in 1540. Contemplating the math got me to thinking about money and its value.

Most people are familiar with the comparison of a million to a billion when expressed as seconds on a clock. If you were to count dollar bills without stopping, one for every second on the clock, it would take you approximately 11.5 days to reach 1 million and approximately 31.5 years to reach 1 billion. That is a pretty huge difference and a fun exercise using a calculator to drive home that point. However, the numbers don’t carry a weight or familiarity for most people, maybe even rich people who possess the amounts in question. This got me thinking about some more practical examples of describing wealth.

A dollar bill is 6.14 inches. Approximately 2 of them in a foot.  There are 63,360 inches in a mile – It takes 10,319 dollar bills lined up end to end to reach a mile. Earth’s circumference at the equator=24,901 miles – so if you lined up dollar bills end to end, it would take 256,958,853 of them to tie a ribbon around the planet. What if they were \$20s instead of singles? Well, you’d have to be a billionaire because you’d need approximately \$5.2B to stretch a ribbon of 20s around good old Earth.

We won’t get to the moon by stacking billions of one dollar bills, but it will get us pretty high. A million of them stack up to about 333 feet (more than a football field) and a billion amount to 63 miles, which is technically beyond the 50 mile boundary demarcating the end of all remnants of Earth’s atmosphere where space begins. It takes 10 crates of \$100 bills to make up a billion dollars.

Are rich people just ignorant or are they so used to being rich that they don’t think the same way that ordinary mortals think about money? There are nearly 15 million millionaires in the United States. Among them, are approximately 36,000 households who’s wealth exceeds \$100 Million. At 60 years old, I’ve been contemplating a few things, though I don’t dream about winning the lottery. I don’t even waste money on such things as the lottery, but it does cause one to contemplate. What if…?

Say I was one of those 36,000 people with assets to burn – and I mean literally! I might live to be 90 years old, so if I could spend \$10,000/Day for the next 30 years, I would  burn through approximately \$110M. That is a bunch of consumer spending – enough to stimulate an economy of a small country. Richard Branson, where are you dude?

Can you imagine having the resources to spend \$10K/Day? You’d need a day off once and awhile. Maybe you only spend \$5k one day and come down with a cold for a week or so. After forking out for your household staff, the butler, chauffeur, cook, and private jet pilot on standby etc, you’d still be holding on to many thousands per day (yep, I know, I left out the part about property tax, but I’m sure my accountant would have a loop hole for it, so I’ll pay him his due).

At the end of the day, as Brits often remark, there are a heck of a lot of folks right here in the United States of America with way too much money. I suspect that most of them haven’t a clue what to do with it. I’d bet quite a number of them have never graduated from college or even high school for that matter.  Are they smarter than the rest of us because they are wealthy? Maybe you will leave a comment. I have my own opinions.

The Gig Economy and Work From Home non-scam-scam

Last week while I was away from home and with time to kill, I stumbled on an article about the best places on the internet to make easy money. Most of the lists were composed of the same sites, such as Respondent and SwagBucks (one of those “you gotta spend money to save money sites). Another that popped up on several lists was Slice The Pie, which is an on-line survey site where participants get paid for their opinion.  Oh and let’s not forget working from home as a proof reader.

I live in Portland, Oregon where there are a bazillion coffee shops within blocks of my house. Within them are slews of 30 somethings lounging on couches and low slung chairs, sipping java and pecking away on laptops. Until last week, I wondered what these coffee house lounge lizards might actually be doing – writing the Great American Novel came to mind and so did using a free Wi-Fi and an app called WireShark to spy on other laptop users. But I was wrong. It seems there is a whole world out there on the internet exploiting the unemployed.

Respondent claims they will pay for your opinions once per week via PayPal. So does REV, which is a SF based service that employs the masses to transcribe audio and video tracks for slave wages (one needs only to examine what is required to discover just how laborious it is to produce an acceptable transcript – way below pennies per word – more like pennies per paragraph).

Gleaning through the lists and visiting some of the sites hosting this sort of work landed me on several blogs that hyperlink to the same sites. The bloggers are all trying to gain passive income by using the hyperlinks as referrals to get \$ for folks signing up to do surveys and some of the other gigs.

Does it actually work? Can a person make \$ this way? Many claim to. We will see.

The Grand Canyon – 5 Days Below the Rim (Fall ’19)

What do you say when a friend calls and asks if you’d be interested in hiking the trails of the Grand Canyon? “Why, yes of course,” I said, forgetting to ask about details before agreeing. It didn’t occur to me to inquire about the particulars such as duration, miles per day, or even specific dates. None of that mattered. I am a hiker at heart and haven’t been to the Grand Canyon for more than a decade. My calendar was cleared and I was already mentally putting together an equipment list.

I’m not sure where the tradition came from. Trail hikers, in particular, Appalachian Trail hikers and Pacific Trail hikers all have trail names. Presumably trail names are given to a person by fellow hikers while out in the wild. One-Mile, who earned his trail name on day three, took on the role of guide due to his vast experience and genuine passion for anything and everything that can be learned about the Grand Canyon. He procured our permit, organized an itinerary, and headed up the logistics to ensure all 5 of us in the party were able to convene at the South Rim of Grand Canyon the evening before we set out. Paratus was the only member of the party I’d ever hiked with but knew right away that an outing with One-Mile, Big-Foot, and Chair was going to be epic.

The last hours of daylight warned that if we wanted to reconnoiter and view some of our route from the rim, we’d need to get a move on. My first look at the Grand Canyon was breath taking, awe inspiring, and all the other words one could come up with to cover the mix of emotions one experiences when facing the immensity and scale of so much nature in one view.

The Geologic Museum on the South Rim was the perfect place to gain some orientation. It was still open when we arrived, giving us a chance to trace our route on the enormous raised relief model, which sits in the center of the museum.

Our route had us departing from the Hermit Rest trailhead, down along a ridge to the Colorado Plateau (more of a long accordant terrace), where we would join the Tonto Trail and traverse and wind to the East before looping back up the Bright Angel trail. Our itinerary included a couple of side trips as well.

From the rim that first evening, we were able to see the section of the Bright Angle we’d be hiking on the last of our 5-day outing. The encampment at Indian Garden looked close enough, but the vertical distance was tremendous. Due to the immediate drop at the rim, I couldn’t see the trail leading up from Indian Garden. I couldn’t even imagine how it was possible for a trail to cling anywhere in the vicinity, to the steep walls of the canyon.

As we continued our reconnaissance along the rim, we stopped at a spot just above a place aptly named “the Abyss.” Though it was possible to see portions of the Tonto trail winding along the plateau thousands of feet below, there was no trail going up or down. The Abyss is a sheer wall of sandstone that terminates some 4,000 feet below the rim. Here we watched the sun set and toasted to a successful and enjoyable hike.

The next morning while waiting for the shuttle bus to take us to the Hermit Rest trailhead, I told One-Mile that my 60th summer 2020 was on the near horizon, and I was planning to thru-hike the John Muir Trail (JMT). One-Mile said he’d just come off a section of the JMT the month prior and that we should strategize about equipment, mileage and such. Paratus was standing next to me, his pack resting next to One-Mile’s on the bus stop bench. I’ve known him for almost 30 years. Paratus is a thinker and per his Latin trail name is always prepared. He does everything right and when he is unfamiliar, he defers to the experts. Paratus’s pack is a carbon copy of One-Miles, down to every detail including three one liter “Smart Water” bottles used for storage and filtering.

I bantered with Chair and Big-foot on the 20 minute bus ride to the trailhead. Bigfoot lives in Las Vegas not too far from One-Mile. Together, they’d done a few other trips, but this was Big-foot’s first in the canyon. Chair is Big-Foot’s cousin, his pack is bigger than everyone else’s. Having lead several Boy Scout trips, Chair is used to having to carry extra things and didn’t seem concerned about extra weight.

When we got off the bus, it felt like we were getting a late start at 9:30 am. The chill of the October air had already been replaced with arid warmth. One must stay hydrated when doing anything in an environment like this one. We topped off our water bottles at the top of Hermit’s Rest, hefted our packs, grabbed trekking poles and set off down the trail. Those first easy steps were quickly transformed by terrain that demanded ones attention.

At 59 years old, my joints don’t handle impact very well. I don’t think I could hike Hermit’s Rest trail or any like it without my trekking poles. Within the first mile, we were spread out along the trail, each at his own pace. I found myself comfortably stair stepping down the steep terrain at the back of the line and nearly stepped on what looked like a fake Halloween spider. Only it wasn’t. This one was big, black, fuzzy and moving ever so slightly on an exposed rock in the middle of the trail. I hailed everyone back so they could look at the spider. Not because I thought they’d find it interesting, rather for my own sake, “you should have seen the huge spider I nearly stepped on…!”

For most of the morning, the switchback trail was sheltered from direct sun exposure by walls of the South rim. Half way down Hermit trail, there is a fresh water spring draining into a trough. There wouldn’t be another water source until we reached Monument Creek, so we filtered and topped off our water bottles.

After a long descent, we arrived at the junction of the Hermit and Tonto trails, where we found ourselves hiking beneath a blazing sun without any cover. Though temperature of the October air doesn’t come close to what it would be in July, all of us felt the additional toll it took on our energy reserves, slowing our pace for the later half of the first day’s hike. I carry an ultra-light hiking umbrella for such occasions, but we found ourselves hiking in a rather stiff fall wind, so the umbrella was of no use.

The Tonto trail snakes its way along the contours of the canyon. A couple hours on the Tonto and our party was stretched out, each of us meditatively solo hiking. We all reconstituted at the top of a short steep descent named the Cathedral Staircase, reminiscent of the kind of steep spiral staircase one might encounter in the bell tower of a medieval European cathedral. By the time we reached the bottom, we were at the base of the Abyss, the wall we’d looked down over the evening before.

The final miles lead us around the corner of a landform that shaded us from the early evening sun. I was surprised to see so many other groups of hikers at the designated camp area of Monument Creek. All of us had exhausted the contents of our water bottles, so once we located a passable camp spot (there were only a few left), we filtered water for rehydrating both ourselves, and our freeze-dried dinners.

I could tell Chair and Big-foot were happy to shed their packs. Chair got his name after we discovered that he’d carried a folding camp chair along with his essentials, which explained why his pack was heavier than everyone else’s. Chair places high value on camp comfort, so we teased him relentlessly over the knowledge that eventually he’ll be lugging it up the Bright Angle.

Each of us located flat sandy spots big enough for tents/shelters. The evening air was dry and warm, so I elected to cowboy camp atop a Gortex bivy bag. I had to admit I felt weary from the day’s exertion. I didn’t anticipate how difficult hiking in the Grand Canyon could be. My weariness was remedied once we’d pitched camp and One-Mile prepared guacamole and chips for all of us to share while boiling up water for dinners.

When you are deep in the Grand Canyon, down in a ravine with a semi-dry creek running through it, and the sun dips below the rim, darkness comes in stages. The final stage feels like a light switch is suddenly flipped off. Stars twinkle and within a quarter of an hour the sky is painted with astral dust. The only sources of light in camp are the glow from cooking stoves and the occasional red beam from someone’s headlamp.

With the exception of Chair, who sat in his chair, the rest of us sat on flat rocks in a circle around someone’s camp stove. I was so tired from the hike and my knees cried out for me to get up from the low rock and stretch out flat on my bivy. It felt heavenly to lay there looking up at the dark sky speckled with stars.

Moments later I heard voices and a rustling of critters followed shortly by Paratus and One-Mile shuffling their way toward my location. One-Mile was chuckling and said something to Paratus, I thought it might have had to do with my meager sleep system. Moments later I find out what they were talking about was the skunk they’d chased out of our camp area. One-Mile was torn between the humor of the situation and concern over what might happen if the thing had sprayed someone.

Paratus settled into his tent and before either of us fell asleep, we heard sounds of critters everywhere, including a rustling near our packs. We both got up, re-assessed what we had in our Ursaks and went through everything else, to include trash, Luna Bar wrappers, empty zip locks that held trail mix, etc. All of this we added to our Ursaks. With that chore complete, the sounds of nature settled into a rhythm permitting a restful sleep. That is until I awoke in the dim light of early dawn. When I looked up into the low tree branches above me I saw several little mice running through the branches the way squirrels usually do.

As the morning light flooded the camp, the mice disappeared. By the time we were all up and about finishing breakfast, the other hikers camped nearby had since left. We immediately relocated to the best site in Monument Creek. With everything in order, we stuffed water bottles and lunch snacks into our daypacks and headed down to Granite Rapids. The 3-mile hike out and back followed the creek bed down to the Colorado River.

We spent the day dowsing ourselves in the river and lounging on a beach by a calm stretch of water. This late in the season, there was very little river traffic. We saw one group of kayaker’s supported by a team of rafts. Big-Foot earned his trail name when we discovered he was keeping his blisters to himself. We heard no complaints from happy go lucky Big-Foot. One-Mile came to the rescue to assist Big-Foot with some preventative treatment.

We arrived back at camp in the shady light of early evening. Big-Foot provided each of us with two “minis” of our choice for a happy hour. We decided we’d do a happy hour with one of them at Monument Creek, and save the other for Indian Garden.

With a nice buzz going, by the time we were finished with our respective dinners, the sky was dark and the stars were popping with a brightness only found in the remotest places humans travel. We spent the next hour or so star gazing and spotting satellites before the cold of the night drove us into the warmth of our sleeping bags.

The Monument Creek campsite is situated about 400 vertical feet below a ledge with a set of steep switchbacks leading up to the Colorado Plateau and the Tonto trail. Anticipating the high temperatures of the day, we headed out at first light to cover as much distance on the Tonto as possible before the relentless sun could do its work.

The Tonto twists and turns its way in and out of the various landforms making up the intermediate depths of the Grand Canyon. There are no safe water sources between us, and Indian Garden, so each of us was weighed down with at least 3 liters. There is majesty to the canyon. The way natural light casts contrasting hues of color against the blue sky of an Arizona morning can only happen in such a place. I overheard Paratus and One-Mile conversing in a low tone. “Desperation,” said Paratus. That is what he told One-Mile he was feeling amidst the formidable terrain of the inner canyon.

There is enough lore regarding the unforgiving nature of the landscape in Grand Canyon to fill thick books. In fact there is a book titled, “Death in the Canyon,” that catalogues nearly all the canyon’s fatalities to date.

One-Mile related several of the stories of hikers and runners who’d over estimated their capabilities and underestimated the environment. Some fell, some simply lost their way and died of dehydration. The moment harkened back to the pre-departure safety briefing that One-Mile gave us before setting off on the Hermit trail. “There is no easy way to obtain assistance while in the canyon,” he said. Paraphrased, he told us there would be places we’ll be traveling where, even with rescue underway, an injured person may land in grave danger and become a danger to the entire party.

One-Mile is a self-reliant hiker. Having solo hiked the canyon on occasion, One-Mile is familiar with and manages risk with a cool head. Though I personally enjoy being completely unplugged while out in nature, I recognize the value of incorporating technology where it makes sense. One-Mile carries a Garmin In Reach and solar charger. It has a capability of sending status reports, lat/longs, and other data via satellite. It serves as a piece of mind, not just for the members of the party but for the loved ones back home to know that all is well at the end of each day’s hiking.

In the later hours of the morning, the inescapable sun began to do its work. I was very glad I had the portable shade of my umbrella. I tried strapping it to my pack so that I might be able to use my trekking poles, but the trail wound around and around resulting in changing sun angles while I hiked. The trail on the plateau was smooth enough that I stowed the trekking poles in favor of shade. It was a good decision. I was in my own world at my own pace hiking the remaining miles into Indian Garden.

Indian Garden sits in an oasis at the junction of the Tonto and Bright Angel trails. It is a busy place, overwhelmingly busy after hiking the Tonto. Even though our permit guaranteed us a site, I discovered there were only two left. Since I was the first to arrive, I staked out the better one for our group. The others arrived a little while later. All of us were exhausted from the trek in the sun. After pitching camp, One-Mile suggested a swimming/bathing spot nearby, “maybe a mile,” he said. Reflecting on the reconnoitering I did on the way into camp, I couldn’t imagine a spot on the creek big enough to immerse in, so I elected to clean up in the shallow stream near our camp and remain behind. The truth is, I was exhausted and had no desire to put my boots back on.

One-Mile got his trail name because after the hot dusty trek, the others lusted for the opportunity to immerse in the swimming hole that One-Mile spoke of. I didn’t see the four of them until the sun began to set and that wasn’t because everyone enjoyed bathing for an extended period. The short out and back one-mile hike wasn’t quite the case either.

This scenario reminded me of my surfing days. Surfers standing on the shore assessing a set of large waves peeling over a reef, will often state the wave height as follows: “looks like maybe 5-6 feet,” when in reality the wave heights are in the teens. So long as one doesn’t have to paddle out to experience their power, it is a way to sound cool. However, One-Mile isn’t that kind of guy. He just wanted to share with his friends, every aspect of the canyon that he loves.

The evening at Indian Garden began with a happy hour. Each of us consumed our second “mini,” which Big-Foot” so graciously provided (though we carried our own). Before turning in, One-Mile produced a miniature deck of cards and we let him slaughter us in a few hands of Hearts.

There is nothing quite as wonderful as a restful sleep after a day of exertion. I cowboy camped atop the picnic table beneath the open shelter and looked forward to waking refreshed the following morning. What I didn’t know was just how quiet mule deer can be. Our packs were hung well out of reach of critters and our Ursaks were stowed in the metal bear box provided by the park service. What could go wrong? It might have been the heavy breathing coming from deer nostrils that stirred my sleep. I woke startled by the face of a juvenile buck slurping its tongue inches from my face. Fearless and almost domesticated, we saw an entire family of these animals living in Indian Garden.

Regardless, I was well rested and so was everyone else. I can’t quite remember how far One-Mile said our hike down to Phantom Ranch and back was going to be, but actual distance had to have added up to a bit more. We hiked down the “Devil’s Cork Screw.” At the bottom Paratus struck up a conversation with a man picking up trash off the trail. He was wearing a “Retired Air Force” hat. Generally, the trails and campsites in the Canyon are free of signs that people had been there. However the Bright Angel is the most traveled in the canyon. The final stretch at the bottom clung to a sheer rock wall on the southern bank of the Colorado. Soon there were two bridges leading across to the settlement at Phantom Ranch.

With a little luck and reasonable fee, you can make a reservation, ride a mule down, and stay at Phantom Ranch. There are several small cabins and a communal dinning room with a small convenience shop with postal service included. Unless you’re staying at the ranch, full meals aren’t available. We were, able to procure a beer, some snacks, a fresh apple, and postcards. I wrote/sent one to my wife which was stamped on the back, “Delivered by mule from the bottom of the Grand Canyon.” The label on the IPA beer that I drank had a map of the rim-to-rim trail drawn on it.

Rested and having consumed one beer, some salami and apple for sustenance, we filled our water bottles and headed back up to Indian Garden. Paratus and I hiked up the Devil’s Cork Screw together. Paratus peeled off at the one-mile swimming hole, which is more like two miles from Indian Garden, and waited for the others.

Hiker midnight comes at around 9 pm. Our little camp was asleep by mid-night. Our final day in the canyon consisted of 4.5 miles of elevation gain back up to the South Rim. Big-Foot and Chair hit the trail just prior to sunrise. Chair wanted some additional leeway to catch an early flight back to his working world. The rest of us followed about a half hour later. We all wanted to be at the top before the sun could do its work.

The stretch of trail between Indian Garden and the rim is divided into mile-and-a-half sections with rest shelters, vault toilets, and water at Three-mile House, Mile-and-a-half House, and Indian Garden at the bottom. On the way up, we blew by the first stop. Halfway up I was feeling every switchback. The trail itself was surprisingly smooth. Just before reaching Mile-and-a-half House, we ran into a pack train of people riding mules. On the way up, we also saw evidence of some trail maintenance.

One-Mile and I were feeling a bit smug about completing our adventure without returning with any uneaten food. Paratus chimed in and admitted he still had a couple sealed packs of tuna and a fresh zip lock full of trail mix. From the bushes below the shelter came a voice, “I’ll take it if you don’t need it,” he said. Within moments, a young guy with long hair and a quirky tick vaulted up the steep stairs leading to the stone hut. The young man was seasonally employed by Mercy Corps and headed a trail work party made up of at risk youth.

Less than an hour later we were standing on the top of the South Rim and within minutes were greeted by Chair and Big-Foot, who had enough time to retrieve their vehicle and stow their packs. Both of them already looked refreshed and ready for anything. One-Mile then offered to buy everyone a celebratory ice cream before we went our separate ways. In all, we had a successful and fulfilling adventure.

The author, (Professor), Scott H. (One-Mile), and Mike C. (Paratus), are former USAF colleagues. Chuck S. (Big-Foot), Scott and Mike are pilots for Southwest Airlines and John M. (Chair) is an Attorney from Ohio. The author still isn’t sure how he got his trail-name.

Backpacker’s Secret Spots: One night out in the North Cascades

As a recently retired person who loves hiking with my dog, I decided to take action on a day dream.  The day dream I used to enjoy involved a realization that with perfect weather on the perfect day, I would drop what I was doing, pack up and go.  Finally I said to myself, “why not.”

A couple of years ago, a friend shared with me his notes about a secluded lake with a trailhead about an hour and a half from my home.  I couldn’t locate the place on any map in my possession but with the notes I had, I was pretty sure I could find the trailhead.  Preparing and leaving was a simple matter, I keep nearly all my backpacking gear handy and packed.  I added a couple packets of freeze dried meal fixings from a large stash I keep around, measured out some kibble for the dog, added some herbal tea bags, packets of freeze dried coffee, filled a water bottle for the hike in (I usually filter the water I’d consume from a local source), and tossed everything in the back of the car.  I asked my furry little buddy to hop in and off we went.

Once we were off the main highway, we only saw one other vehicle, headed the opposite direction. Less than 2 hours after leaving Portland, we arrive at the trailhead.  It was a Wednesday afternoon in late summer and no other vehicles were parked at the trailhead.  Not a soul or sound in sight or within earshot either.  Only a few smudged footprints were visible in the pine dust when we started the short trek in.

The trail itself isn’t very long or difficult.  In my experience, these types of hikes usually lead to places filled with remnants of young people’s outdoor parties and all that goes with them – trail trash, beer cans, fire pits with partially burnt refuse etc. But…this was different, totally and unexpectedly peaceful, clean, and pleasant.  I suspect only a few people have even heard of this place and those who know of it, respect it and “leave no trace” of their visits.  With my dog Matisse leading the way, we contoured around to a shallow ravine where we could hear the sound of Green Lake Creek cascading down the draw to the White River 5 miles below.  I carefully stepped across some large stones in the creek, keeping my feet dry while Matisse slogged across slurping while rehydrating himself.  Most of the trail wound along the contour with a couple of detours around recently fallen timber from the previous winter (lots of fallen trees everywhere – this past winter provided the north cascades with a particularly heavy snow).

To my great surprise, we arrived on the lake’s shore at about 3:00pm.  The only sounds came from a raptor hiding in the high branches of one of the many pines lining the lake.  Between the large bird’s infrequent squawks was the rhythmic sound of wavelets lapping the deadfall along the shore accompanied by the buzz of aquatic insects dancing over the lake’s surface.  I thought that maybe since it was still early there might be some late arrivals – maybe even a large group.  With that possibility, we decided to pitch camp and take in the peace and quiet for as long as possible.

I used to have different gear for back packing.  Most of my stuff was ’70s vintage and reliable, but also bulky and heavy.  I’ve also discovered that at a certain human vintage (mid-’50s) one can hike faster and farther with less weight.  I’ve since ditched my old gear and acquired some pretty nice lightweight and durable equipment that makes my outdoor adventures even more rewarding.  In all, my entire outfit weighs in at less than 25 lbs.  That includes hiking poles (double as shelter frame), hammock (I use it as a lounge chair mostly), and ukulele (my 22 lb banjo would blow my entire pack light strategy).  With my current arrangement it takes about 10 minutes to set up or strike camp.

Catalpa Lake

By 6:30 pm, the sun cast a long shadow over the lake and as it sank below the west ridge, caused the water to go still.  I prepped some kibble in a collapsable bowl for my dog, then set about making dinner for myself.  The Jetboil stove had 2 cups of water boiling inside of 45 seconds.  This I poured into a pouch of Beef Stroganoff, which I stirred and resealed in order for it to rehydrate for about 20 min.  I then filtered some more water and boiled it up for tea.  It wasn’t a gourmet meal, but in the out of doors, everything tastes good.

With sunset, I determined we’d be the sole residents of this wonderful secret spot in the North Cascades.  I thought this kind of solitude could only be achieved in the off-season, but I was rewarded with the unexpected.  Morning unfolded in reverse order with peaceful solitude prevailing throughout the entire experience.  I’ll be heading up to Catalpa Lake again in a couple of weeks – on a Wednesday afternoon for sure.

Book Review – Hound of the Sea: Wild Man. Wild Waves. Wild Wisdom by Garrett McNamara

Deserves to Be Read (4 out of 5 Stars)

McNamara’s surf memoir is a worthy read if only for the fact that he was the first to conquer surfing a 100 ft wave.  This work chronicles McNamara’s life from childhood through the present.

With respect to non-fiction memoirs written by prominent personalities from the surfing world, I make it a point to read them all.  Unlike other athletic pursuits, surfers rarely take time to write about their sport.  Hound of the Sea is a story written by a surfer for surfers.  The title is a reference to the author’s Celtic surname meaning “hound of the sea”.

Unlike Finnegan’s Barbarian Days and Duane’s Caught Inside, McNamara’s story doesn’t come across as a literary, colorful, masterpiece of prose.  Nearly all the chapters are 5-6 pages long that address specific milestones or memorable moments in the author’s life.  The first 77 pages seemed pretty unremarkable at first, but later it was clear how the early non-surfing years of the author’s life gave shape to his life goal “To Keep Surfing”.

What I really enjoyed about reading this book was the honesty and mater of fact transparency the author so humbly offers to anyone interested in really knowing what it is to walk in his shoes (or more appropriately his flip flops).  Among the elite few who’ve ever surfed “Jaws,” “Teahupo’o,” “Mavericks,” or “Cortes Bank” to name a handful of monster big wave spots, at one point or another, these surfers all discover that what they do in the water is like living in a fish bowl.  The chapter titled “Incident at Cortes Bank” is one example of how the opinions of non-witnesses and media could really crush a person’s spirit.  This was a really important passage and I’m glad McNamara chose to include it.

What I didn’t enjoy reading about was the cavalier attitude toward including marijuana and other drugs in the surfing lifestyle. True as it may have been for McNamara, it is sad and disappointing to be reminded that not every surfer (even those who are tremendously accomplished) is a clean living, serious athlete.

In the end, what worked for me as an admirer of Garrett McNamara was the “blue print” he developed to become the kind of serious big wave rider who is worthy of historical recognition.  In the realm where McNamara operates (riding enormous killer waves), one cannot imagine how these surfers are able to keep fear in check.  In his words, brief and concise, on page 219, McNamara says, “Fear is something we create, because we’re stuck in the past or envisioning the future.  If we stay in the present there is no fear.”  Coming from a man who’d endured the physical trauma of having his body tortured from the thousands of pounds per square inch and being pounded on reefs countless times, there is no question that Mr. McNamara has the credibility to speak to fear.

McNamara’s work is a testimony that even a crooked path can lead to greatness if one remains humble and sticks to their “blue print.”