Wondering what ya'll carry for readin' and writin' and o' course 'rithmetic.

Do some carry books? Notebooks? Calculators? Pen fillers or pencil stubs?

Do you keep notes on your trips as you go and if so where do you write it?

I've been taking a little pen and notebook in my map bag. Doesn't we much (2 ounces?) and it's nice to have somewhere to write notes down. Most of the trips are scouting for later so I hate having to resort to memory after the trip and forget something important.

Little tiny notepads. Sometimes overpriced products from REI, sometimes the smallest, cheapest notepad I can find in a 7-11.

My favorites were these notepads distributed to fire crews (forest fires). Waterproof, fifth-inch graph paper small enough to fit in a shirt pocket. And the standard firefighter rules on the back.

I either use a little mini-pen or (more often) a pencil stub). Sometimes I like to take larger sheets of paper and some crayons. That can be way fun.

Why do I carry writing instruments: journals -- it is pretty lame if you just record where you hiked, how far you hiked, how much elevation you gained or lost, and what you ate (although even masters of the art like Shackleton would let their accounts degrade into something very like a cookbook. An extremely bad cookbook). Better if you add polemics about why the human race is mostly hopeless, why horses hate people, or why USFS wilderness management policies are either the first sign of the collapse of the American Empire or the death of the American Republic. Or both.

I almost always make a shopping list of things to bring on my next trip. Sometimes I consult that when I get home and go out again. I also like to make little sketch maps and take notes as I travel off-trail so I can find my way back when I am exhausted and it is foggy or completely dark.

Sometimes i carry reading material. Especially if I with a group or suspect there will be a lot of down-time. Reading material I like to carry:

_Accidents in North American Mountaineering_. 'nuff said. Makes great reading when you are tentbound and lost in snowy mountains.

_Weekly World News_. How do they make that stuff up? After a few weeks the _New York Times_ is as ridiculous. Even the ads are funny. Also makes a great firestarter.

Natural history guides. I like _Cascade-Olympic Natural History_ by Dan Matthews. 'nice to know what those mushrooms you are eating actually are.

For really, really long trips with a lot of expected downtime (like a month in Nepal, say) I'd like to carry two paperback books. Hopefully I could trade with others en route when I was done.

When I was studying for my EMT, I carried my textbooks and actually read them on long weekend trips.

Edited by david_bonn on 12/08/2006 18:08:36 MST.

Notebook: Moleskine Cahier. Small, flexible, lightweight, and very high-quality paper.

Pen: Lamy Safari Charcoal with fine nib. It's not weatherproof or pressurized or anything special like that. It is light, easily refillable, and, most importantly, is a fountain pen that feels so good to write with.

What do I write about? Mileage and such are ok, I suppose. However, I mention them only briefly, if at all. What seems more important is the absolute beauty of being outside and the clarity that it brings to the mind. So, anything goes. Old memories that suddenly resurface, the way the stream beside your tent is gurgling, the color of a wildflower you passed, musings on teleology...

Since there seems to be an endless number of things to write and think about, I generally don't take anything to read. If I'm in a very new ecosystem, it's often nice to take a book with good summaries of the geology,biology, etc. particular to that habitat.

>Wondering what ya'll carry for readin' and writin' and o' course 'rithmetic.



Readin': Backcountry First Aid and Extended Care, 4th ed.; Tilton, Buck; Globe Pequot; 2002 (2.5 oz). This pretty much covers the Wilderness First Aid course material.

Writin': I'm not much into journal writing, but when my mind relaxes I'm never sure what will pop up. And if it's something boring (e.g., work I need to do) I want to write it down then forget it until I get home. Fisher Space Pen, Stowaway model (0.2oz); Rite in the Rain All-Weather Writing Paper (50 sheets bound with covers: 1.8oz; five loose sheets <0.1oz). Both are available at REI.

'Rithmetic: I work it in my head. If it's complicated, I work it twice or compare with estimates to confirm correctness. Square roots are especially fun :) I can chew up lots of hiking time this way...

readin: small Bible or a New Testament with Psalms and Proverbs added in.

writin: i don't - at least, when on the trail

figgurin'/rithmetic: me noggin'

Reading: "Tiny Testament" New Testament

Writing: Pencil and 1/2 small spiral bound notepad.

Calculating: If my phone is with me, that has a calculator, I try to avoid math in the woods as much as possible. That tiny bit of math necessary for navigation, I do in my head.

It depends on the trip. If I am looking at tent time, I bring a thin paperback novel to waste time. I have been known to upload podcasts and books on my I-Pod and take that instead. The few time I have taken paper, it was a small notepad I found, and a mini pen.
It is the book I miss if I don't take one! Worth 3-5 ounces.

I love to read on the trail. For the last 2 1/2 years, I've worked full time as a teacher, part-time at REI and studied full-time for my master's degree. Needless to say, recreational reading has taken a backseat to educationally mandated text. So when I'm out there, I push my body and rest my mind.

Occasionally I read novels. This past summer, I bought the full volume Chronicals of Narnia and split it into the seven different books, each going in to a maildrop for my Colorado trail hike. It was heavenly reading, particularly in the first couple of weeks when there were absolutely no other hikers out.

Other times, I carry a small guidebook for my next big adventure, and I build a broad range plan that I can refine later on. This Christmas time on a six day trip in the Smokies, I'm taking my guidebook to cycling the Natchez Trace, and I'll form my plan for roughly where I'll stay on various days and what I can use as alternates, as well as determining important points of interest that I'll want to add time for. The Trace ride is in late March. No better time to start preparing than now.

As for writing, I like to be impractical and carry a bit heavier personal journal. It's more attractive and doesn't look like every other yellow waterproof journal on the trail. I carry a pen and pencil, in case the pen runs out or freezes.

Rite in the Rain waterproof paper in a refillable binder (so I can take the right number of pages for the length of trip), and a mechanical pencil.

On my Alaska trips, I write in my journal pretty religiously (every night), focusing on the story of what happened that day. Then when I get back I type it all up and stick it up on the web, along with the trip photos:
www.aktrekking.com/trips.html

I started keeping journals on my first big trip (800 miles down the Alaska Peninsula in 2001). I found them invaluable afterwards, since you can never quite recreate the perspective of being in the middle of something when you're back in your living room. And I can use them to write stories and articles afterwards.

On my next big trip, I'm planning to post some of the journal entries to a blog every week or two (when I'm in a town) so friends and family can keep up with me. (It'll be a 9 month expedition)

Of course, all the paper may end up being not so UL. But I also carry a digital SLR and a couple lenses, which is really not UL. It's all about what you want out of the trip, I guess.

-Erin
www.groundtruthtrekking.org/WildCoast.html

Edited by mckittre on 12/09/2006 12:22:20 MST.

Miles, very nice stuff. Both the pen and the notebook look pleasurable to use. With writing materials like that who needs to read?

Edited by romandial on 12/09/2006 16:55:11 MST.

Erin,

What are the dimmensions of the paper you write on? Do you use pen or pencil?

Do you take notes during the day, as things happen? If so, where do you keep the notebook?

Or only at night in a review sort of way?

Do you write thinking of certain people who will be reading your notes? Who?

How do you deal with the chores if you are busy writing? I mean does Hig do dinner and you do breakfast so you can write in the evening?

And we all love your writing as you know:)

Lets see... The paper is 4.5 x 7 inches, and I write with a mechanical pencil (normal pens won't work on waterproof paper).

I don't often take notes during the day unless they're logistical sort of notes. (someone's address if I'm in a town, a GPS point for a photo I need to be able to locate exactly, etc...)

Usually, I wait until after dinner or any chores, and write from inside the sleeping bag. So it's a review of the day. The result is that I get a little less sleep than Hig, but we're usually sleeping long enough that it doesn't matter much, and I can make him do more of the morning organization...

I'm not always thinking about it directly, but I guess I try to write most like I'm telling the story to a friend. (which I'm bad at in person, so I like to do it in written form...)

-Erin
www.aktrekking.com/trips.html

I take a small notebook that is less than 1/4 inch thick - and has dimensions of 3.5 x 4 - for a pencil I take a small plastic mechanical pencil.

I like to take note of the temperature, weather and other little things in point form. This makes it easier to write my trip log when I get home.

I write on the back of my maps, printed off the TOPO! program, if I write at all. Just in case of emergencies I carry a small, thin, pencil -- like sometimes used to come with hanging kitchen frig note pads.

I write on my maps; here's how:

For long treks, I usually create custom maps (with NG Topo!). I first import them into Photoshop and adjust the levels to make the colors and countours "pop" a little. Then, I add a box of semi-transparent "whitespace" to the map in a noncritical location that I'm pretty sure I won't be navigating through. That box becomes my journal for the day. Each map usually represents "one day" of trekking (~20 miles). Towards the end, as mileage increases, I will have two maps per day.

I size my maps for an edge-to-edge dimension of ~11" x ~11"*, print maps on double sided paper and order them numerically, e.g., Day 1, Day 2, Day 3a, Day 3b, etc.

* Sized so they fit into a 12x12 Aloksak with one/both map views available without opening the bag.

The maps usually get printed on regular copy paper (light!). If I'm going with heavy waterproof papers (like the plastic stuff from Nat Geo), I have a writing challenge: most writing implements smear on the plastic type papers. This bites for journaling and writing navigation notations.

I like the Rite in the Rain paper for writing, but for map printing, it's expensive and heavy. So, I like regular copy paper: cheap and light. When I'm done printing, I usually go one step further, hang the maps from a clothesline, and spray them with Rain-X or Scotchguard.

I keep my maps handy, and then write things throughout the day on the neat little half transparent boxes that I photoshopped into the map image.

Sometimes, if I can spare the weight, I'll add a tiny notebook to the mix, mainly for writing non-route-related things in camp (like comments on why a particular piece of gear wasn't working, or a shopping list for the next trip, or just to solve some DE's here and there for mental stimulation <-- "geek!"). When I take a notebook, I use a Rite in the Rain #391-M mini notebook, sold here at BPL <-- "pimp!"). BUT I also really like a little floppy Moleskine, which is about the same thickness and a little bigger, because the writing paper is nicer and it has a little pocket in the back I can use to stow a leaf or flower petal or a laminated index card that contains key phone numbers, calling card number, credit card number, resupply logistics info, whatever.

For a writing instrument, I use either the Nalgene waterproof pen, which writes on virtually any surface and bleeds less than sharpies, and a pencil. I like a pencil because I can erase and it works in the rain.

If I am trekking a new off-trail route, I always bring a set of fine point waterproof drafting pens: red, blue, green, and black, for detailed navigation notations. I use the various colors for different types of notations.

I have a short (4") mechanical pencil (0.5mm) that I picked up from somewhere (who knows?) that I really like because it's convenient and stays sharp.

But for nostalgia, I more often just carry a golf pencil or two with an eraser head and sharpen it as I go with a small sharpener.

OK, so what do I write about?

1. Lots of navigation info.

2. Animals I see - but more importantly - the unique behaviors they were exhibiting at the time. On my arctic trek, I noted not just a bear, but the groggy bear that stood up and looked yummily at Roman; or the Jager that dove down and nicked my hat becuase it was defending its nest; or the wolverine that ambled along the river bank, stopped, looked over curiously at us, and then ambled on its way. He had the same voice as Crush the Turtle in Finding Nemo. I wrote that.

3. How my gear is performing, and how it makes me ... f ... f ... feel...

4. Ailments. These are most often about my feet.

5. Unique experiences throughout the day. "High ridgetop winds - hard trekking!" or "Swampy tussocks coming out of XXX basin" or "Found spike camp - log stool was comfy!" etc.

I don't write much polished narrative. Here and there, I will, in order to record the philosophy of the moment, so to speak.

I like journaling a lot. It's a rewarding part of my trekking experience.

Edited by ryan on 12/10/2006 12:46:05 MST.

I always carry my modified version of Zen and the Art of Motorcycle Maintenance with me when I'm hiking. For journal I bring a 2" x 4" spiral-bound notepad and a golf pencil. I recently purchased a 1.3 oz. digital voice recorder which I'm interested in trying out as well.

Like Sam, I've been carrying a recorder as well. I have a really nice stereo recorder that picks up the sound of a "butterfly landing on a leaf" (sorry, not really, but I received an email this morning from somebody telling me that my product reviews were written too dry...).

I recorded the arctic wolf sound that was on NPR with the audio recorder on my Pentax WPi, but the wolf was really close. With my other recorder, I was able to pick up wolves howling around my camp in Yellowstone. They were on either side of me, but probably 1/2 mile away, and the stereo condensers picked up both channels. It was really cool to listed to with stereo headphones.

I've also been doing some "wilderness recording" for some audio shows that BPL is producing, and the stereo channels are neat, because they can pick up the two conversations (as in an interview), separately, with the wind of the trees on the one side and the burbling of the brook on another. I love this stuff.

It's an Edirol R-09 and weighs 5.1 oz with Li batteries. It has SD card storage so I can store music, audiobooks, sounds clips from my son or wife, etc.

Edited by ryan on 12/10/2006 12:55:06 MST.

Like Miles I also journal in a Moleskine - I switch between the small reporters journal and the standard pocket notebook...trained as an illustrator, I prefer blank open pages to rules, esp. as I can sketch what I've not photographed or draw routes. I love using 0.25mm Pilot pens I get in San Francisco's Japantown...something delicate and intimate about writing...very...small...and...slowly... ;-)

Ryan's post reminded me: I am two weeks away from a sea kayaking and hiking trip to southern Thailand, so I am borrowing a friend's minidisc recorder with stereo lav mic's that clip on to your sunglasses (or similar), to get human-ear-distance stereo separation. In the middle of the jungle at night, it should be fun!

DrJ,

all i can say is "Wow!".

you have it all down to a science. very impressive to say the least.

solving DE's aka DiffEQ aka differential equations - you sure know how to party when on the trail, you party animal you!!


lastly, you reminded me of something that sounded very familiar...

>>"I have a short (4") mechanical pencil (0.5mm) that I picked up from somewhere (who knows?)"

been lookin' for mine for some time; thought i had misplaced it at work.

Ryan, for you and other ULers ....., a linear, first order and separable differential equation with initial conditions.

Enjoy.

Edited by romandial on 12/10/2006 13:56:46 MST.

Roman, I'll have to get back to you on that one. I'm number 7 on the wait list for Diff Eq next semester. We have been doing some DE's in Circuit Analysis, but nothing quite like that. Hopefully I like Diff Eq better than Calc....

Adam

First, is there a right answer to this? And, if we find where the hiker is at the end of 24 days do we get a gift?

Second, is this in the same vein as the edible gear. And, does it make a difference if the edible gear is packed in a vacuum sealed canister or not? i.e. does the vacuum lighten the load? And, what would be the shelf life of said edible gear if dt>ds and we hold it constant for s(0)=0?

You bet there's a correct answer! And with all the education and sophistication among the posters and lurkers at BPL, at least a dozen of you should be able to solve it handily.

As for prizes......?

Ryan,
I have an Edirol R-09, too. I'm a composer and do a lot of electronic manipulation, so I use it for that and recordings for ethnomusicological research. I hadn't thought of taking it backpacking, but now that you mention it.... I'm definitely going to try it! The sound is absolutely great for such a small device, and with a 2GB card, you can fit a lot of audio.

About those recordings... is BPL thinking about starting a podcast or something similar? That would be great, and I'd love to help. I know quite a lot about recording technology, audio editing, music composition, etc.

Well done Roman, this question seems to be a model for a recent unsupported long distance hike.

It haven't solved these equations in perhaps 7 or 8 years, but my initial calculation gave this as a result:
s(t)=14t + t²/2 with s(24)=624.

Toms right:

Here's some further explanation

Its first order separable, linear equation that does exist and have a unique solution.

First we move the dt to the right side, which gives us

ds = 14dt + tdt

Then you take the integral of each term, which gives us

s = 14t + 1/2t^2 + c

The constant of integration was left out by Tom, but since it comes out to be zero izzz all good.

Plug in the initial condition.

0 = 14(0) + 1/2(0)^2 + C

C = 0

s = 14t + 1/2t^2

s = 14(24)+1/2(24)^2
s = 336 + 288

s = 624 miles

Come on Roman is that all you've got?? Send me one that is at least a second order linear that only exists around a regular singlular point....ok??

:D

Yes 624, but what is the connection between 624 and 24 and Roman?

624 was the easy part.

Edited by rogerb on 12/10/2006 15:49:01 MST.

You guys are great. I love this site.

24 days and 624 miles were the end points of my experience on the Arctic 1000.

While I had hoped to eat ~2lbs/day and improve our distance by ~2 miles/day, as I'd found from adventure racing, it actually came out to reduce by 2 lbs/day meant that we could go 1 mile more per day.

Possibly this latter result was because we made 12 hour days the norm rather than 18+ hours as in adventure racing.

And Crazy Pete: very well done...but know I have yet to come up with a good second order DE that we might feel pertains to us....but I will work on it!

Edited by romandial on 12/10/2006 17:10:01 MST.

After Ryan mentioned taking mechanical pencils in another thread, I found some mini mechanical pencils at a Walmart Neighborhood grocery store. They are in a pack of 5 pencils, just under 4 inches and are Foohy brand...for less than 2 bucks.

I got the following after first Romanizing the equation. Starting with the original Romanesque Equation I first got:

DS/DT = XIV + T

Divide and multiply by D/D, then (S/T = XIV + T) BY D/D.

Assuming D is not 0, then D/D = I. Then I times (XIV + T) = ITSELF or UNITY. In other words it is a unified disintegrated differential equations.

Then S/T = XIV + T OR T = (XIV + T)/S, if you divide both sides of the equation by S.

Thus, s(0) = O could not be true unless T = 0. So the only possible answer is that given by other scholars and trekkers who would know what the starting factors, location, and variables were (which appear to be Roman's appetite and food budget for trip in the Arctic). One would, therefore, make the assumption that the range of probable, if not possible answers would include the farthest distances one could go and the least simultaneously -- fulfilling the requirement of diminishing simultaneous returns in closed dietary pack systems, not otherwise providing for the possibility of negative distances or 0 -- requiring that there be a positiev but uncertain resolution to the equation.

If the equation were to be subjected to further testing and field experience, possibly deserving an article here or in the print magazine, then the numerical probability would probably be more certain and one could then hypothesize both an absolute maximum, the mean, median, and even negative limitation points -- such as those sugggested by Pondering in the unpublished treatise "Negative Distance Effects of Hunger: The Simultaneous Distance Quandry of Positive Distance Traveled Total Miles Trekked Diminishing In Returning for More Food Events."

Also, as a secondary numeric anomaly, since T is iself equal to itself, a period of Time spent hiking for 24 days, with s(0) = 0, can only lead to a conclusion that d = d during the particular time as empirically measured and not deduced.

Therefore, the concept or mathematical idea that s or t leads to a change in location (d) is only a theoretical possibility in a range of locations from 0 to 624, based upon actual calculations and observations by trekkers in this time-space reference frame.

The ultimate conclusion: 624 is the best available solution, but is subject to human error and will require both verification by the BPL Staff who should weigh in with a study with thermometers, calibrated walking devices, and photographic evidence. The more likely conclusion, based on this equation is that nobody is getting anywhere fast. Even that is questionable within the ranges of possible, though not probable sets of whole integers resolving the equation for s(t) at the conclusion of 24 days.

BD-- I am not exactly sure what you are doing, and I believe that you have made some simple mathmatical errors. First off, what exactly are you doing multiplying/dividing by D/D?? Are you just saying that the Ds cancel each other out because they are superimposed over a fraction line?? Because those are demarcations of the process of derivation, not variables, and to multiply by a D is incorrect, unless you are somehow intergrating somewhere else in the equation.

Secondly "S/T = XIV + T OR T = (XIV + T)/S" is NOT true, because when solving for T one would get

S = T *(XIV + T)
S/(XIV + T) = T

Thus your statement T = (XIV + T)/S is wrong.

And if you were actually solving for T in that equation you would factor it out, otherwise the entire excercise would be fruitless.

Thirdly, a solution DOES exist thanks to the Existence and Uniqueness Theorem, and a quick look at the graph shows it to be continuous in the examined area. I am thus confused at your statement that 624 is the best available solution, because it IS the solution for the IVP with given input value.

Crazy Pete,

Oh. Oops. Sorry:) (Do you want help off that rock? Great avatar, by the way.)

I thought the processes or process of derivation was a constant, but the variability over the set of possible processes might itself vary, although not in this case -- given that it is apparently a function or process of Roman's appetite, or any other trekkers or the multiple variabilities of either other trekkers or sets of trekkers dietary requirements or choices. Kind of like econometric regression models of consumer behaviors in the case of scarcity models based on multiple variabilities and differential processes. (*See below comment on the Existence and Uniqueness Theorum.)

Thus the overall apparent aberations from mathematical norms and rules. Also, while the use of S may appear to dictate your version of the equation it is also possible that speed will dimish the dt portion of the equation IMO, thus I chose the diminutive form of dividing by S to find the solution over any given range of T.

Sorry bout that. I still firmly believe that best choice of an answer (your solution) is 624, based on the previously described simultaneous returns quandary. But, I am willing to go along with any solution so long as I do not think about this when trying to go to sleep tonite.

* Re the Existence and Uniqueness Theroum from the University of Texas at the Permian Basin: "There are two important points to make now. First the theorem does not tell us anything about how to find a solution. Finally, we have no idea of how small the region may have to be to accommodate the theorem. In other words the interval of existence for the solution may include little more than the initial value." at http://www.utpb.edu/scimath/wkfield/mod3/Exuni.htm

Edited by bdavis on 12/10/2006 21:45:21 MST.

BD-------
"Then S/T = XIV + T OR T = (XIV + T)/S, if you divide both sides of the equation by S.

Thus the overall apparent aberations from mathematical norms and rules. Also, while the use of S may appear to dictate your version of the equation it is also possible that speed will dimish the dt portion of the equation IMO, thus I chose the diminutive form of dividing by S to find the solution over any given range of T. "
-----End BD

S/T = XIV + T
(S/T)/S = (XIV + T)/S

1/T = (XIV+T)/S
Not T = (XIV + T)/S

T = (-14 plusminus (196-4s)^.5)/2

But this is all subiderary to the fact that what the equation states is that the rate position is changing with respect to the change in time (velocity), is equal to 14 plus t. Which means that the velocity is changing, which is the whole point of a variable slope. The velocity increases as T increases---FOR ROMAN. Whether or not the equation applies to others has no effect on the correctness of the postulate. Say for someone sitting all the time, the equation would be DS/DT = K, where K would be a constant velocity, in this case zero.

As to the E and U Theorem, it does not tell us how to solve for a solution. It gives whether one exists.

The graph of the equation proves continuity:




The interval of existance (-infinity, infinity).

Perhaps I've never learned what you are doing with the derivative--but treating the D as a variable automatically removes it from the equation, just as 3/3 = 1. D/D would be one as well, except it means the first derivative of position with respect to its corresponding first order time. So in essence, I am still confused by what you did...

And waaaaaaiiit a minute--- time is the INDEPENDANT variable here. You don't calculate time based on distance, but rather distance based upon time.

Edited by crazypete on 12/10/2006 22:36:46 MST.

Crazy Pete,

How about you? Have you done any UL modeling you can share with us?

Crazy Pete,

Quite right.

So if T is independent, then the issue becomes is the 14 correct if the equation is to work for the generalized equation for a trek of many people or individuals or people sitting at home.

One question, how do you get to:

T = (-14 plusminus (196-4s)^.5)/2

That may be my problem, even though this started as a kind of fun spoof thing for me, I take seriously what you are saying because my food could depend on it or people's safety.

I think the issue is, mathematically, you cannot include enough processes, differentials, or variables in different levels of mathematical process to make a formula that will work in this example. Although the usefulness of them is that they will prevent disasters by predicting a range of values which will work.

Again, while I was spoofing at first, thus the reference to the made up unpublished treatise, you guys are right on ... I just don't think the "theorum" or "formula" or "equation" will work in realtity.

Thus, like Godels proof, even within a mathematical system let alone when it is applied to realtiy, the system cannot generate its own proof, or in the case of the general theorum of existence of unique solutions, this may be a kind of tautology. Input in = input out, or confirmation that given the intitial hypothesis there will only be one answer, regardless of the realities the formula is trying to measure. Does that make sense to you?

This is starting to interest me so much I can't stop thinking about it, but no harm meant on my side. I wrote a spoofy answer and got back what is expected at this site, a really great answer.

Update: T may not be independent, because of the length of time travelled each day, or the length of time it takes to travel x distance, or some other function of time, even though it is a constant as we measure it. Thus, c becomes important in your equation, because it may not be zeroed out because s(0)=0. So the question that really starts to loom, and I was afraid of this given my mind and interest in this, is: if c, in your equation cannot be established without empirical data, can it be cancelled out ... and can s(0)=0 for more than one set of facts????

Edited by bdavis on 12/10/2006 23:47:22 MST.

Roman-- Not really theoretical stuff like this would be, but simply stuff like force on tarp panels in various wind speeds.

BD - I used the quadratic formula to solve for T.

The C is the constant of integration; briefly, that means it is similar to a y-intercept in that it moves a line up and down. We graph velocity vs time, where the slope is acceleration to determine total distance traveled by area under the curve. By the initial given condition, that S(0)= 0, C = 0. All this initial condition means is that the 0 distance has been traveled at time 0. If you start at say 5 miles already having been traveled, then S(0) = 5 and C would be a value other than 0 due to the face there is more area under the curve.

The great thing about the integral is that it takes into account that the distance traveled each day can be different, as hmmm let me make a graph.



OK, in the graph you can see that the velocity is constantly changing, just like you said. As such, a different distance is traveled everyday, but this can still be accounted for. The hard part is getting the equation for this line, which Roman provided. Everything else is (somewhat)simple mathmatics.

That said, I would not be able to use this for any acutally applications on reality due to the fact I do not have a formula for DS/DT.

Edited by crazypete on 12/11/2006 00:12:27 MST.

Crazy Pete,

Cool. Trying to put math around this UL stuff is cool, way cool.

I never thought of doing it. But I only have myself for a sample/null set v. sample. Thus you guys are way ahead of me on that one, and much more.

I think the problem is your null set or model will require, mathwise, some 15 people to make the N (or in your equation ultimately "c" valid). Then the "C" or "c" and the 14 will work in combo.

Then you can develope a functional equation that is correlated to reality for specific real groups or individuals. (Given the caveat that it won't work on any given day -- the curve margins.)

My first thought is what needs to be done to make it work, to establish a curve, like Roman has started or suggested, you need to create a model of each function: DS and DT. (Thus your comment that DS/DT does not have a formula or reality at present -- to me that means empirical data + thought.)

I believe it can be done and that is what this site is for, we just have to control for or establish what the ranges are for individual people or sets of people, trekkers, or whatevers that the DS/DT will apply to.

Then they will have to hold to a particular projection or model of behaviour to make the math fit the reality???

Edit: That is why I zeroed out the d function. If it is the same graph/curve for an individual or small group, then it is the same over T.

Further update: The velocity problem is exemplified by the graph you just providedl Given the variabiltiy, draw a line from the bottom and top points the range of values gets to be too great to continue it with any meaning. What I noticed is the line goes downwards. ????

Edited by bdavis on 12/11/2006 00:46:20 MST.

DS and DT is simply a ratio of two different rates. All we need is a representation of how one's velocity changes over time and then one can figure everything else out.

I believe that finding this curve is impossible though.

The C and the 14 are unrelated. The 14 was just a part of the velocity equation Roman stipulated. The equation for others may involve a t cubed or rooted or a t cubed plus t rooted. The C is just a marker acknowleding that there are infinite solutions to a differential equation, and depends completly upon the initial value, and won't change for different people.

What changes is the velocity equation, and as such, their constant of integration depends only upon whatever inital value they plug in.

I updated my previous communication, just saw yours. Agree, for now anyway, thus I can actually go to bed. Thank you for the dialogue and thought, most persevering and percipient.

Edited by bdavis on 12/11/2006 00:49:40 MST.

I do hope no-one takes any of this seriously!

OK guys, now try to find the analytic solution to an elliptic integral.

Edited by rcaffin on 12/11/2006 02:49:36 MST.

Roman, see what you started!!!

BD, your humor was immediately apparent, either that or that lengthy appeal brief you were working on fried your gray matter. I'm still trying to figure out if CP knew from the outset that you were joking around. I think that he knew, but chose to deal with it as if it were serious, but i don't really know for sure.

I'd really like to see more from CP, who to my way of thinking is NOT very crazy at all. Good job, CP.

Oh, and PETE, you don't mind if i call you Pete, do you? (or is it Mr. Pete?), one word of advice, quit while you're ahead. BD, is a lawyer. You simply can't win with a lawyer. Even if you do, they just file another appeal! I really enjoy talking to attorney's, but they're a little like the Hydra that Heracles/Hercules fought. Slay one head and two heads pop out to take its place - that's the way it is with their arguments, slay one and they come back with two more - clever folk that they are.

Edited by pj on 12/11/2006 03:06:47 MST.

Only if its definite Roger....

:D

Oh and one final quick reply---the velocity vs time graph was just an example that may or may not apply to anyone's walking speed.

The variability of the velocity is not a problem. Just think of that graph as one of you and your car, except without stoplights. All that graph is giving us is different velocities at different times. We use integration to stack an infinite number of rectangles under the line to calculate the area under the curve, thus giving us the total distance covered.

pj, et al. -

Quite right that Crazy Pete is not crazy .. that is certain. In fact, I wish he could graph and create algorithims for law office scheduling efficiencies.

Ditto on the lawyers, hopefully trekking around will curtail the appeal upon appeal phenomenon, because of physical exhaustion if not new found common sense. Hope springs eternal.

I'm not even going to touch Rog's suggested new math project, leave that entirely for CP and RD. As Roman said earlier, what a really great group of amazing people hang out in the SUL/UL/L realms. Back to the trenches for me, may all have a great day and lighten their loads.

So here is a graph of the model's solution plotted against the Arctic 1000 mileage data

And here is the best fit which gives a slightly different relatiosnhip between walking speed and day as

ds/dt = 19.9 + 0.52 t.

Notice that around day 10 we drop below the "average" and again at day 22.

At day 6 and 7 we hit the really good ridge walking.

And to keep on thread: these data were recorded on 1:250,000 scale USGS paper maps with a pencil stub.

Roman,

(Wrote this before the second graph, still looking at it.) Did you have a goal of so many miles a day? The points and curve are very 'symmetrical' or consistent.

At the end what caused the jump in miles per day, or it appears there was an increase over the norm? Did the terrain become easier to negotiate or did you travel longer hours?

IMO this shows the trekkers were in good shape and that the terrain didn't matter, they made their 20 or so miles a day, regardless of the time it took on a daily basis. Is that true or was the hiking time the same, you mentioned something about that? With you guys all being experienced and in good shape it may be that you covered the 20 or so miles regardless of terrain or elevation shifts.

A model of my distances per day would definitely show that I cannot get that far over rough terrain or an elevated hike in one day at a consistent rate. What I see this as showing is that trained, in shape trekkers can create a consistent day to day distance over time, regardless of terrain. A real goal and way to measure my success, also shows a strategy for covering the distance in a given time.

What you and CP are doing is very helpful to me in evaluating my own performance, health, fitness, and concept of what I am doing "out there."

Edited by bdavis on 12/11/2006 22:27:14 MST.

BD,

BTW you had me laughing out loud with your comments and the exchange with CP. It was as if you two had orchistrated a straight man funny man act. Good fun. I was L-ingOL (or is it LOL_ing?) over your convolutions.

IN the two graphs the dots are what we actually did and the curves are the models.

The only goal we had each day was 12 hours of travelling, although we did go more than 12 and less than 12, of course.

The points climb more steeply at the end because with a lighter pack we could go further, both faster and longer -- that was UL backpacking at its best.

Of course the terrain did matter -- swimmimg rivers and snowy passes slowed us down. So did bear detours and tussocks. But the big picture shows a consistent, but somewhat weak, trend of going farther, faster as the trip progressed, not just becasue we were stronger, smarter, more driven (because we also had less chocolate, more difficult travelling, and more sore feet) at the end, but because we could move more easily -- hence farther each day with the same amount of overall effort.

If you were to go on a long hike and record the distance walked each day and plot the distance from the start, your curve would likely look similar. Your initial distance per day may be less, so your average distances per day would also be less, but the slightly upward curve to the data points would be there for you, too, I reckon.

Anyway, thanks for indulging me!

Some like to tinker with gear, I like to tinker with the relationship between my body and Earth's landscapes and to interpret them in a variety of ways -- analytical as well as emotional.

Edited by romandial on 12/11/2006 23:00:12 MST.

Romano,

You're cool. Hope CP didn't take offense at the baristorial convolutions; I actually never took the calculus (although I read some commentaries on it by Leibniz when I was studying philosophy -- after quiting biochem). I spent my time in probability, statistics, sociometrics, and multiple regressions -- did read the theoretical math journals in the library at college once in awhile when I was playing hookey from my job in the library offices on summer breaks. But CP and you reawakened it all, and CP is good at it.

I think the minor shifts on the graph can be major in reality at the upper end -- two miles or ten miles is a big distance when I am approaching the end of a trek, especially if the terrain is going to be bad like walking through volcanic cinder for a mile in order to get to my car.

Most of all the graphs are, IMO, a confirmation of training, fitness, experience, gear quality, lightitude, etc. If I could get a performance graph like that I would kiss the beautiful earth next to my car door at the end ... on my way to get a burger and fries after a longish trek (or long for me).

Edited by bdavis on 12/11/2006 23:44:51 MST.

> on my way to get a burger and fries after a longish trek
YEAH!

Coming back to the original question. I use my Swiss army knive to write.

What?

Yes, Swiss Army knive, this one:

http://www.victorinox.ch/index.cfm?site=victorinox.ch&page=196&lang=E&highlight=altimeter

It has a pen in it. And:

1. large blade
2. small blade
3. corkscrew
4. can opener with
5. - small screwdriver 3 mm (also for Phillips screws)
6. cap lifter with
7. - screwdriver 6 mm
8. - wire stripper
9. reamer, punch
10. key ring
11. tweezers
12. toothpick
13. scissors
14. multi-purpose hook
15. altimeter
- 100 m – +6000 m
- 300 ft – + 18000 ft

16. thermometer
- 20° C – +60° C
-0° F – +140° F

17. pin, stainless steel
18. mini-screwdriver ( pat.)
19. woodsaw

How's that for multifunction?

Eins

Edited by EinsteinX on 12/13/2006 08:13:38 MST.

Eins, looks like a great little knife.

They make a relatively tiny mini SwissChamp (i forget the precise name, but i think it's MiniChamp) with a pen too, but it doesn't have the all of the gizmos that yours has. I bought one after my accident when it became clear that i was becoming forgetful and couldn't remember things like i used to. Problem is, it's in my pocket, out-of-sight-out-of-mind and i forget to use it!

I carry the small moleskine notebook.

I usually bring my Creative Zen Nano Plus MP3 player loaded up with audible books and podcasts. I try to read this way. It is nice too, sometimes to listen while walking that last 5 miles.

pj,

I have a swiss army knive for 12, 13 ? years now. I couldn't live without it. I almost carry it everywhere. I got this one (it's my 3rd swiss knive) because of the altimeter.

Eins

I carry a mini RITR notebook in my front pants pocket and a Inka pen hanging from my pack strap so I can take gear notes as I go. If I'm going SUL I just bring a space pen cartridge and carry it inside the notebook. I switched to the RITR even though it's heavier than plain mini notebook paper because it's hassle free (no need to worry about keeping it dry) and keeps a permanent record more handily than regular paper. (I used to staple my trip log to my gear and food list when I got home. Now I just file the RITR notebook when it's full.)

When I'm going to do some real writing I stick a sheet of printer paper in the book I'm carrying. I love to read outside, I found it really relaxes me and inspires "revelations" because my brain is "off," not because of what I'm reading. If I bring a book, it's usually a mindless romance. My last trip I departed from romances and read Richard Adams' sequel to Watership Down.

One reason I backpack is to get away and turn my active mind off. Romance novels don't require a lot of thinking and work perfectly to enhance my mini-spa in the wilderness.

For me it is the mini RITR notebook and for a pen, it is the small pen in my swiss army knife. The pen is small and reliable whilst carrying a spare is easy, not losing the spare pen is the challenge.

Maps are also great for notes, its keeping track of the notes and maps when you get back home is the challenge.

How do people store notes from trips, electronically and hard copy or ...?

Roger,

My notes are all on maps. Sometimes I am able to transcribe the notes to TOPO and keep them electronic. But usually they remain on the map....

second all those above who say writing is important- I consider my notebook a survival tool, and am a sanity risk without it. Cheap ones tend to be light ones-small school exercise books, or breast-pocket sized jotters from corner-shops. I write with a biro, for reasons of permanence, ubiquity and cheapness.

I used to write in the long candle lit evenings in my tent, but since going over to the light side I've ditched both candle and tent and spend my evenings in a bivvy sack, which only has space for iffy, paranoid thoughts in it. I hope the evening writing habit will return when I've finished my tarp project and once more have overhead shelter. In the meantime writing tends to get done in cafes, on public transport, and on the more comfortable rest stops during the day.

I write whatever I have to to let me sleep. Hopefully this will be present beauty, meaningful details, or the insights that distance and aloneness can give. Often it is just the nonsense that I can no longer spare head-space for!

Zen and the Art is a wonderful book to read on the trail. I've baulked at the weight for shorter trips, but for a longer hike I'm planning around south west England and Wales next spring, I may ditch my camera in favour of Mr Pirsig's words!

as someone marooned on the romantic side of the Cartesian rift, I've just read the middle page of this thread and was horrified. Needless to say I didn't get the joke...

...I use fingers for most of my calculations, and limit my calculations to those that can be done on fingers...

That would be a digital calculation?

To pass the time, in my head I calculate the gravitional perturbations of my backpack on my cranium, and the perturbations of my cranium on my backpack. (I am a perturbed little man.) I assume a centrally symmetrical, static gravitional field, degenerating at infinity. When gravitional potentials are applied, from them the energy tensor of the matter in my cranium can be calculated on the basis of the field equations of gravitation.

Robert,

I think you need to get out more. Perhaps you could try hiking with other folks.

I'm not allowed to actually hike: they roll me along like they did Anthony Hopkins in "Silence of the Lambs."