--- Language Resources ---

If people go by their experiences in school, "Language" is probably thought of as vocabulary, grammar, and. maybe, literature. Foreign languages would be included in all that. But there is a lot more to it than that. Those communications classes - those are language, too. How about etymology? That's one of my favorites. I almost enjoy being criticized for saying "Call a spade a spade," so I can explain where the phrase comes from and why it has absolutely nothing to do with race. Or, when I say that "It's all balled up," and some one looks at me like I said something dirty.

That's one of my favorites. When people relied on horses to get around, they would often ride, or take their carriages out on a snowy day and the snow would get packed under the horses hooves into tight snowballs, causing them to fall down.

Likewise, "to suck" derives from the beat generation when, if you were a good trumpeter, you "really blew" but, of course, the opposite was to "really suck."

There's more to why a particular person said /that/ than choice of words. Sigmund Freud actually did first describe the Freudian slip - saying something you really mean without intending to go quite that far. There is certainly a psychology of language.

And language is composed of signs. Words are signs, but people don't always associate all those other signs as language - but it is. Semiotics is the study of signs. There is  much more to language than people usually think and much of the most fascinating parts are often ignored.

Why does the English "father", the German "fader",  and the Italian and Spanish "padre" sound so much alike; and why doesn't the Russian "otets" and Aramean "hayry" follow suit?

Why do Americans gesture with the first finger and thumb of one hand in a circle to indicate that things are alright, and why will that get you into trouble in other parts of the world? Our nonverbal language is also language.

I mentioned two of my favorite authors of linguistics in the blog, "Language and me". You might also want to check out Desmond Morris' Peoplewatching. And if you want to check out the languages of other folks - horses, dogs, cats - he's also written Dogwatching, Catwatching, Horsewatching, and Animalwatching.

"Foreign language" is a relative term. German may be foreign to an English speaking person but not to a German speaker. English is a foreign language to many people in the world. Ironically, though, English is a langua franca, so it is understood by many people whose first language isn't English. I learned German in college because, at that time, a lot of research in psychology (my field) was published in German. There are a lot of reasons to pick up another language, but one is just that it's fun to do so.

If you want to devote a significant part of your time to the serious study of language, you will certainly need a reference library and you couldn't do much better than the online MIT reference library (https://libguides.mit.edu/c.php?g=176227&p=1160775).

And if you want to pick up a new language, check out MIT's OpenCourseWare offerings in foreign languages. For supplemental study, fun, and games, look at the Digital Dialects page (http://www.digitaldialects.com) and the BBC's languages page (http://www.bbc.co.uk/languages).

If you want to delve into sign languages, there are many resources for American Sign Language on the web. I recommend the excellent AMSLAN dictionary at Signing Savvy (https://www.signingsavvy.com).

I'll be looking into a lot of language while I try to learn Spanish this year. Maybe you'll get bit by the language bug.

Is there a foreign language you have always been wanting to pick up? Just keep in mind, the longer you wait, the harder it is to learn it. Don't let the opportunity slip by.

Walk around town and pay attention to what people  say. Do some of the phrases they use seem odd to you? When you really think about it, do many of the phrases you use seem odd to you? Why do people say those things?!? Most dictionaries have the etymologies of the words - explanations of where the words come from. You can usually find the origins of phrases on the Internet.

--- Spanish ---

A funny thing happened during my first session of Spanish. I suddenly became emotional. I'm not that kind of guy! Things don't usually move me that way. I hope it's a good omen. Watching the video felt...joyous.

One session for me is about three days. I start with the Class Activities list on the MIT website, watch the video episode, and then complete the textbook assignments. The next day I do the activities in the workbook. The third day I play around with the supplementary materials. I have all the resources in a single file - here's what it looks like in Windows explorer.

                                                                        [Spanish explorer]

And I keep all my notes in a LibreOffice spreadsheet one page to each session.

At this speed, I may be able to finish the first MIT course in a year. Hopefully I'll be able to talk with my Hispanic neighbors (with only a little good natured laughing.)

--- Math in my world ---

I've avoided mathematics heavy curricula. One consequence of mathematics as a language is that my dyslexia interferes with mathematics also. I'm slow and make a lot of errors, but one of the advantages of math is that there are always checks. If you know how to check your work, there's never a reason to let an error in calculations get by you.

But I enjoy mathematics. I especially enjoy explaining mathematical concepts to others. I like opening up the mathematical machine and showing others how it works.

I took courses in college through integral calculus and I continue taking them via the Teaching Company, MIT OpenCourseWare, and other resources. One of my areas of specialization in graduate work was research methods (the other was vocational evaluation.)

I haven't done a lot of research, mostly helping others with their projects, but I have done a good bit of advisory work and think of myself as a pretty good statistician. I like teasing information out of real world data.

One of my long term projects is the software I offer in my website, the Therian Timeline. I'll be talking about that as time goes on. It's available in the Excursions section and there's a link in the Related Pages links to the right on this page.

Research is an issue in the therian community and I made these tools available as free downloads so amateur researchers could have easily accessible tools. I continue to build on them. For instance, DANSYS is a LibreOffice Calc spreadsheet (Calc itself is a free download) that can already perform most of the commonly used statistical procedures, but the extended version, DANSYSX, can do far more. I'm currently working on a regression procedure that will build a best regression equation from a set of data, rejecting weak variables. That one will take a while for me to complete.

Some folks love numbers; some hate them. What about you?

--- Language and me ---

Me and language? Language and I?

(Head slap) It's not even a sentence! Forget it!

What do you expect. I'm an animal. (Movie reference)

I'm dyslexic, I think in images, I stammer, I occasionally can't pull out the words I want to use, and, yes, I talk to my self.

Verbal language is not my first language.

But, then, my contrariness has served me well more than once. I have always been fascinated with and have enjoyed those things that I am not supposed to be able to do. That's why my favorite x-sport is rock climbing (or, it was until I clocked up so many hand injuries that my grip has gotten weak. A rock climber climbs with their hands, not their feet.) and rappelling.

I was not good at language so I was in two gospel groups and two advanced church choirs for many years, have two minors in world literature, joined the speech troop in college, and have spoken publicly....a lot. If you can find the Auburn Circle from the 1970s, I have stuff published there. The Circle is the Auburn University literary magazine.

I can tell you stories...and I probably will.

I'm not much for board games (they bore me), but if you can drag me into a game of Scrabble or Pictionary I will be ecstatic. I love crossword puzzles, Cryptoquotes, puns....people say that puns are low brow. They're wrong. Puns are perpetrated by people who love language and, consequently, love playing around with it.

Double talkers slay me - luckily there aren't that many around any more. The last two I can think of are Archie Campbell (if you haven't heard his "Rindercella", you must find a copy and listen to it.) and Norm Crosby. I'm sure there are others around, I just dropped TV when they went to high definition.

My favorite linguists are James Kilpatrick and Bill Bryson. Kilpatrick was actually a journalist. Wikipedia calls him a "grammarian" - I beg to differ. A grammarian would never say, "If you understand what I'm saying, then I'm using correct English." A linguist, on the other hand, would. He had a popular newspaper column on the English language for many years.

Bill Bryson wrote a book about an attempt to walk the Appalachian Trail (A Walk in the Woods). He's a professional author. He also wrote The Mother Tongue, Made Here in America, and Bryson's Dictionary of Troublesome Words.

I can speak a little German (a very little and very slowly) and can read considerably more. I still have a little American Sign Language left. I'll probably brush up on them some day. Just now, I've started a last ditch attempt to learn Spanish. The MIT OpenCourseWare course I'm using is fun - I'll see if it's effective.

As you get older, it's harder to pick up new languages. I have a friend who is my age that makes it a hobby. I think he's got 20 or more that he can speak conversationally, but he does it constantly and has been learning languages for many years. I still have hope.

How about you? Are you a "language person?' What's your story?

--- Lookout Mountain data ---

They say that atmospheric pressure and temperature drops with increased altitude. The relationships are complex (See the Wikipedia article for Barometric Formula for the pressure equation) but we don't have to be exact here. Pressure drops about 11.3 pascals for the first 1000  feet above sea level. A pascal is a measure of pressure that is equal to one Newton of force over one square meter of area, or about 0.000145 pounds per square inch. A millibar is 100 pascals.

On my recent hike up Lookout Mountain, I carried a weather meter with me that measures barometric pressure, temperature, humidity, and quite a lot more. As for atmospheric pressure, it will measure to a tenth of a millibar, or 10 pascals. It measures temperature to a tenth degree Fahrenheit. I stopped occasionally to record the time and altitude from my phone, and the atmospheric pressure and temperature from my weather meter.

The weather meter is a SensorTech by Dakota Watch Company. I bought it several years ago from the National Geographic products catalog. Here's what it looks like.

                                                              [My weather meter]

There are several ways that altitude can be measured. The only way I know that it can be measured with precision is by a couple of surveyors with expensive equipment physically hiking up the mountain. Smart phones can do a decent job. The most accurate phones use an onboard barometer that can compensate for temperature. My phone doesn't have a barometer but it will give me a reading by the less precise method of GPS. One global positioning satellite can give a pretty precise fix on a location by latitude and longitude (horizontal position on the globe), but to get an altitude for a point, there needs to be at least two satellites. The altitude is triangulated between the satellites (there's trigonometry involved). With all the calculating, some accuracy is lost, but I've compared my readings with altitude contours from topographic maps and they tend to be pretty accurate.

My altitude measure for the starting point of my hike was 5764' and it was just below the 5800' contour on Google's topographic map. Windy Gap was at 6941' and the Google topographic map showed it to be just above the 6900' contour.

Here's the data I recorded.

                                                             [Lookout Mountain data]

And here's a graph of pressure and temperature vs. altitude.

                                                            [Data chart]

See the problem?

Actually, I noticed part of the problem while planning the hike. I wanted a day with stable weather because as weather systems move through, as you probably know from weather reports, barometric pressure changes. I didn't want the barometric pressure changing for anything but altitude. My meter was barely sensitive enough to register the difference between the bottom of Chimney Gulch Trail and the summit of Lookout Mountain as it is.

Imagine my chagrin when I noticed that, according to Dark Skies, the weather service I commonly use, there is a dip in the barometric pressure every day around noon! Why would that happen?

The weather station I was watching is on Colfax and I'm sure that street heats up as the sun rises. Hot air (think about a hot air balloon) is lighter than cold air. Golden is a smaller town but I expected some of the same effect. What happened? Here's a chart of the altitude, temperature, and pressure over time.

                                                                 [Time]

According to my calculations, my hike had an elevation gain of 1430 feet (for a travel record see the Terminus: Golden blog). That gives an average altitude gain of 8.6 feet per minute, or 513.8 feet per hour. I think my hike up Mount Cheaha in Alabama was steeper but it was only an elevation gain of 95 feet. The temperature curve is so flat I made a separate chart for it.

                                                                [Temperature]

It certainly dropped as I went on. But how did these variables change with altitude? Well, there's the jaw dropper.

                                                        [with altitude]

In the lower part of the trail, there was a slight decrease in pressure, about 0.8 millibar over 1000 feet. Then, Bam! Right around 1000 feet the pressure went up (!) from 954.3 millibars to 965.9 millibars. That is over 10 millibars in the wrong direction!

Well, of course, there's a reason. At 6951 feet, there is a natural wind tunnel called Windy Saddle that collects all the winds from one side of the range and blasts them through to the other side. You can probably guess that compressing air makes it denser and creates more pressure, and, also, that denser air is colder. Right here the temperature dropped from 62.7 degrees to a rather brutal 46.9. I had to put my coat back on!

Air is funny but it's very predictable. Things like the ideal gas laws that you might have learned in chemistry governs it's behavior and, therefore, forms a basis for the behavior of weather. Do you have a wind anomaly like Windy Saddle near where you live? If you visit, try to figure out how it works. Weather meters, thermometers, and pocket anemometers (wind meters) are fairly inexpensive and, perhaps you could record some measurements and make some charts. Feel free to show your results in the comment section of this blog.

--- Math Resources ---

You don't have to have equipment to do mathematics as Arthur Benjamin explains in his book Secrets of Mental Math and the Teaching Company course Secrets of Mental Math (both of which I recommend highly.) but if you want to explore mathematics, you really should have a few pieces of equipment. If you already have a computer and/or a smart phone, many of these tools are free downloads.

I would recommend having a good spreadsheet and there is even a free download for that - LibreOffice (https://www.libreoffice.org)  has a fine spreadsheet called Calc, but most office productivity suites have their own and, if you already have one, most of them work similarly enough that we can all talk about their spreadsheet and understand each other.

I also use Google Sheets on my smart phone. The nice thing about Sheets is that I can share the same documents between my phone and my computer and they don't take up space on either because they're saved in Google's cloud storage.

The nice thing about a spreadsheet is that it can do anything a scientific calculator can do, except it can do it a few million times at the same time (each cell on a spreadsheet is virtually a full function programmable scientific calculator with graphing capabilities and a whole lot more.

But a spreadsheet doesn't substitute for a graphing calculator. Although most spreadsheets have graphing capabilities, they are primarily designed for business and statistical charting. A good graphing calculator is designed to do mathematics. For instance, most spreadsheets won't give you a serviceable polar graph (I've programmed that ability into DANSYSX but there's still a lot that a graphing calculator will do that DANSYSX can't. I'm working on it....) Not to worry. There are two popular (free!) graphing calculators available for computers that will do everything - get them both because they both have they're strengths.

GraphCalc is a great little graphing calculator utility that will give you rectilinear or polar graphs in 2D or 3D, and it works just like a handheld graphing calculator (http://www.graphcalc.com).

GeoGebra is a mathematical visualization utility (https://www.geogebra.org/?lang=en) that has many extensions available, many of them specifically for teaching mathematical concepts. It has grown over time and now will change between a graphing calculator and a mathematical visualization utility.

There are a couple of "analog computers" that I will recommend simply because using them provides exceptional familiarity with numbers and arithmetic procedures.

It's hard to use an abacus without strengthening your mathematics skills and understanding deeply how numbers work. David Bagley has put out several versions of abaci and they're all on this site (http://www.sillycycle.com/abacus.html). Choose one that meets your needs.

To really get a grip on mathematical principles, learn how to use a slide rule. A slide rule will give you an intimate knowledge of arithmetic operations up to and including logarithms. The problem is that slide rules went out of style when scientific calculators came out and so they are very expensive now. On the other hand, there are online and downloadable slide rules available on the Internet. Here's one ( http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html). Derek's Virtual Slide Rule Gallery has several models for you to choose from (http://www.antiquark.com/sliderule/sim). And a portable version of the same is here (http://solo.dc3.com/VirtRule.html)

And I must plug my own works. They are free and I don't even ask for donations.

DANSYS is a spreadsheet built over LibreOffice Calc. It has many mathematical utilities built in and DANSYSX, the extension, has many more. I also offer ToolBook, a LibreOffice spreadsheet that has tools programmed into it such as randomizers, timers, and counters, and over time, I'm programming more into it. Both are available here (http://www.theriantimeline.com/excursions/labbooks). There's other stuff here, too, and I will be bringing that up as time goes on.

There are a lot of other mathematical utilities online for specialized use. For instance, if you want to explore differential equations, there are vector field maps and other visualization tools available.

I'll be showing you some of my toys as I explore mathematics in the field next year.

People ask me why anyone needs mathematics above what they teach in elementary school. My answer is usually that it enriches one's life. Mathematics is fun. If you like puzzles, then you would probably like mathematical problems. Further, there are things that you can probably figure out at home without resorting to college level mathematics, such as scaling recipes, but most advanced mathematical techniques were developed as shortcuts and labor saving devices and understanding them gives you the same advantages. Finally, mathematical knowledge gives you a one-upsmanship advantage in social interaction. Just think of how impressive you will be when someone asks you how fast you drove coming over and you return, "Do you mean average velocity or instantaneous velocity?"

--- Spanish ---

Well, I have my Spanish textbook and workbook and am ready to embark on this year-long (and maybe more) adventure. I'm starting with MIT's Spanish I course, which is available on the Massachusetts Institute of Technology OpenCourseWare site (https://ocw.mit.edu/courses/global-studies-and-languages/21g-701-spanish-i-fall-2003). The online course tells you which materials they use (you have to buy your own but they're not expensive) and provides a syllabus, calendar of activities, assignments, related resources, and in-class activities (which has handouts as PDFs).

I have set up a LibreOffice Calc spreadsheet as a notebook and I have other resources that I will be using including the exercises and games on  the Digital Dialects website (http://www.digitaldialects.com). There is also a (fairly) nearby branch of the Denver Public Library (the Schlessman Family Branch) that has a regular Spanish conversation group. I may attend that once I become a little conversant.

The MIT course uses a Spanish TV series (which can be accessed through the Annenberg Foundation website http://learner.org/series/destinos) as a core learning experience and a companion textbook and workbook. There are 26 episodes and 52 class sections. The course is designed as a semester course but I will be taking more time with it for additional exercises (and because I'm old).

I think I've mentioned that I've tried to pick up Spanish twice before and failed. As you get older, it's harder to pick up new languages. German and American Sign Language were easy and Spanish looks like it should be easy also, and I would like to be able to converse with my Hispanic neighbors.

There are many ways to pick up a new language - commercial and free Internet resources and community programs. It's fun and you can spend as much time and money as you want. Especially check out the MIT OpenCourseWare language courses.

--- End of the year, start of the next ---

I've focused on religion and social sciences during 2018. The physically disastrous end of the previous year left me drained and I haven't regained my endurance completely, but I haven't let it slow me down too much. I haven't made any particularly long hikes but I did, for instance, make it out to Strontia Reservoir, around 13 miles round trip. And I made my second near 1000 foot ascent without much pain. Then I capped off the year with the 1400+ foot ascent of Lookout Mountain in Golden.

There were some big gains during the year. Most outstanding was my gain of a son by adoption and the addition to our extended family of an exceptional little canine. I learned something about family law.

I'm not done with the social sciences. I plan to continue explorations of the local community through next year. That will mesh nicely with one of my planned topics - language. I will be making a (last?) attempt to learn Spanish using MIT's Spanish courses as a core curriculum. It's not the first language that I've added on. I learned German and American Sign Language in college and, although I've lost the ability to converse in either, I can still read German with some difficulty. Perhaps I will polish those languages once I get to where I can talk with my Spanish speaking neighbors.

I will also be playing around with mathematics. That doesn't seem like much of a field subject but, in fact, there is a lot of math in my future. Mathematics is a primary language of sciences and 2020 I will embark on a hands-on exploration of hard sciences beginning with astronomy and physics.

I've already made use of mathematics, for instance, in my study of smiling on the trail. In the coming months, I will be developing trail mathematics and measurement techniques in earnest. For instance, I plan to use surveying skills to determine how tall that huge monolith at Red Rocks is using only primitive tools and trigonometry.

                                                                       [Red Rocks]

I have some larger scale hikes planned. This year the station-to-station hikes have been on the order of less than 10 kilometers. Next year, I plan to check out the ends of the lines (there are 11 destinations). I have already explored the area around Mineral station - Chatfield Lake, Waterton Canyon, and the Mineral to Littleton section of the Platte River Trail - and Golden Station, with my hike up Lookout Mountain. That leaves nine more.

I also plan to hike the Highline Canal Trail in four sections, one for each season. These will be 20 mile lengths but I will start at the beginning (Waterton Canyon) and, since the canal runs on gravity, it will all be down hill.

So, join me for a year of adventure and learning in 2019.

--- Terminus: Golden ---

I took the first E Line from University Station after 8:00 am, transferred to the W Line at Auraria West Station and pulled into Golden Station at 9:45.

                                                                  [Golden Station]

The W Line ends just at the eastern outskirts of Golden at Jeffco (Jefferson County) Government Center. There is a pedestrian bridge over Highway 6 to what looks like apartments and some shops called "Golden Ridge". My destination is the Chimney Gulch Trailhead, which I know to be about two miles west on the south side of the highway, but there is no pavement, so I stayed on the north side and took the 6th Avenue Trail into Golden.

The Jeffco Government Center is an impressive structure with a high central rotunda and grounds that are landscaped into gardens.

                                                       [Jeffco Government Center]

I didn't know how long my hike would take - it proved to be demanding - so I skipped the sightseeing and determined to turn around at 2:00 pm regardless of where I was. I didn't want to be struck on the mountain trail after dark. I will return to Golden when I start back the station-to-station hikes and this building will certainly be one stop.

The walk down through Golden is through parks including one devoted to geology and paleontology - Triceratops Trail - and I see several signs to museums and other points of interest. I'm sure I'll be coming back.

                                                               [6th Avenue Trail]

The North and South Table Mountains are fossil volcanoes that display vertical bluffs of basalt around their rims. (Correction: these mountains are not the actual volcano, but are lava flows that poured from the volcano.)

                                                             [Table Mountains]

                                                          [Triceratops Trail Plaque]

Golden advertises that it's "Where the West Lives" and here's the cowboy and horses to prove it. I did notice a rodeo grounds as the train neared Golden.

I'm not sure what that means, though. There are "Old West" looking buildings aplenty and I'm sure a goodly proportion of the museums are about the Old West, but the people seem pretty modern to me.

I was impressed with how friendly and outgoing the folks in Golden were.

                                                                         [Checkmate]

The statue is called "Checkmate"  and is located in a small park situated on a bridge where 19th Street crosses 6th Avenue.

The iconic "M" on the side of Mount Zion overlooking Golden - a friend once told me that it was where Buffalo Bill Cody was buried. He was wrong. I've also read that it stands for "Mountain" and is there to show Texans what a mountain looks like. Actually, it stands for "Mines' as in "School of Mines' which is a university located in Golden. In 2017, the School of Mines ranks 82nd in the U.S. News and World Report "Best National Universities" and was ranked by QS World University rankings as the top institution in the world for mineral and mining engineering. This school has recently turned it's sites on space as a "final frontier" for natural resources.

                                                                       [The M]

The parking area for the Chimney Gulch Trailhead is on the south side of Highway 6 across from Harry D. Campbell Field. Not knowing about the small culvert cum pedestrian underpass where the intermittent creek that runs down Chimney Gulch passes under Highway 6, I trotted across the busy road, and spent several minutes trying to find the trail. (The underpass is along the small creek on the western side of the sports field.)

                                             [Lookout Mountain from the parking area]

                                          [Highway 6 along the flank of Mount Zion]

I was surprised to see this chunk of rose quartz on the trail. It was much rosier than it looks in the photograph. I left it where it was.

The environment along the lower part of the trail is foothills with grasses and straggly brush and many of the wildlife that I see around Mount Carbon. I didn't see deer but I spotted plenty of droppings.

                                                        [Trail at about 5935 feet]

This trail is described as "difficult" and I would agree but not for any lack of maintenance. The trail is well kept. The difficulty has to do with it's steepness and. perhaps, traffic, although I chose to hike it early on a weekday and did not encounter much mountain bike traffic until later in the afternoon, and even then it was not bad.

All the hikers and biker were friendly, outgoing, and polite. I met three joggers headed up the trail ("Up" - I want to emphasize that word.) I was tired after the two mile hike from the railway station down to the trailhead. Jogging was not even in my range of possibilities.

                                                            [Chimney Gulch Trail]

That's the Coors Brewery to the right.

Chimney Gulch actually is a gulch (in contrast to Harvard Gulch, for instance). It is, in fact, a V-shaped valley with steep walls. It was named for it's appearance after a forest fire ran through it.

                                                                          [Magpie]

I have a hard time getting photos of birds. They will sit there until I get my finger on the "shutter release" button and will fly away. I asked this fellow if he minded if I took his picture and he sat there for a shot. I, of course, thanked him, and paid him $20 (just joking about the $20).

The trail crossed a dirt drive in one of the neighborhoods on the flank of Lookout Mountain and, at that altitude, Denver was in clear view.

                                                                 [Denver skyline]

                                                                        [Broader view]

Golden is in a broad valley between Lookout Mountain, Mount Zion, and Galbraith Mountains to the south and the two Table Mountains to the north. The main stream is Clear Creek so I'm guessing that it's the culprit. It probably gets pretty uppity during the spring.

Further up the gulch, and not very far, there was still ice in the creeks and across the trail.

                                                                  [Bridge with ice]

                                                                 [Ice and snow]

After a while, I crossed from the straggly plains environs into pinyon and Ponderosa pine forests and, here, I noticed that I was looking down on the tops of those two ancient volcanoes.

                                                                 [Table Mountain]

Unaccountably, my pictures of Windy Saddle didn't take. Maybe my phone froze.  I did get this picture of an engine cylinder head at the top on Lookout Mountain Trail. (?)

                                                                  [Cylinder Head]

A saddle is a ridge between two mountains that divide two deep valleys. In mathematical terms, it's a hyperbolic paraboloid (I'm getting into mathematics next year so I had to throw that in.) This particular saddle is evidently a natural wind tunnel since winds blow there constantly at considerable velocity. The temperature dropped from 62.7 degrees Fahrenheit to 46.9, and I had to put my coat back on.

The forests turned to true montaine habitats and, suddenly, I was unmistakeably in the Rockies. There were lots of tiny finches and they would have nothing to do with my photography. They played "squirrel", staying just on the opposite sides of trees.

I considered continuing to the top of Lookout Mountain but, at 1:30 I thought that if I made it, I would want to look around and rest and I wouldn't be able to do much before 2:00, so I turned around and headed back down.

Did I mention that Golden is in a valley. Once I reached Highway 6 I still had two miles uphill to walk to the train station. The train was waiting for me. I sat down and sent my family a message: "I'm on the train. It's not moving. I don't care."

I don't know how high I hiked. I've seen estimates from 1000 feet to two thousand feet. I measured it at 1430 feet but my phone doesn't have an onboard barometer so the altimeter readings are less accurate. The contours on the Google topographic map places the trailhead at about 5800' and Windy Saddle at about 6900' giving an altitude gain of about 1100'. The summit of Lookout Mountain is at 7377', so, according to that, I ended up somewhere between 1100' and 1577' above the trailhead. 1430' sounds about right.

I've read that you can see seven states from Lookout Mountain....wait, that's the one in Tennessee. I've been there, too. If you're in the South, it's worth visiting. It has the only river that runs it's entire course on top of a mountain. That's what the ads say. It also has one of several deepest gorges east of the Mississippi River. And it's where Neil Gaiman set his final climactic confrontation  in American Gods.

There are two Lookout Mountains in California, one in Idaho, one in New Jersey, one in Oklahoma (there's a mountain in Oklahoma?), three in Oregon, and a Lookout Summit in Washington State. There are probably others. You should check out the one nearest you.

I didn't get to check out the eating places in Golden. I will certainly come back to that in the future.

There's a lot you can't see and experience unless you go there on your feet but a hike like this requires planning and a good constitution. Study the area before you go. What is the weather like? The difference of about a tenth of a mile on the Chimney Gulch trail dropped the temperature 15.8 degrees with a sudden wind that would suck the heat right out of you. Carry snacks and don't forget the water. Dehydration is a serious condition on a trail where there is no phone or Internet coverage. Watch your pace and don't overdo it.

Addendum...My cousin from Georgia and her husband visited me Monday, May 2, 2022 and we drove up Lookout Mountain. It was cloudy but I got a decent shot of Windy Saddle.

--- Language and mathematics ---

This year my dual focus will be language and mathematics, but are those really two different things?

There is an ongoing philosophical debate as to whether numbers have an independent existence "out there" in nature. Is there a property of nature called "one"? Is there really a such a thing as a fraction?

Part of my graduate training was in research methodology. I've done a little research myself, mostly as parts of student teams, but I've mostly been involved with helping others develop their studies. Two of the biggest problems I've seen in studies are reification and reductionism.

Reductionism, in this instance, is the tendency of specialists to see their world from the narrow viewpoint of their own area of expertise. A medical issue will always have psychological, social, and environmental elements so a physiologist looking at diabetes might focus on the blood and pancreas and forget all about these other elements, and that can be useful as long as it is kept up front that his results are only part of the story. But if you have to deal with the reality of diabetes, you'd better not forget the other things.

Reification is much more insidious and difficult to guard against - often, it's just ignored.

Science doesn't give truths. It provides models that allow us to understand things that happen in the world and make predictions, but no model is perfect. All models are approximations of reality. A good model preserves as many of the important features of reality as possible so that it's outcomes can be said to be accurate to within certain specified limits. The error can be specified. But there is always error.

We keep models in our heads about how we think the world works. And, hopefully, our models are pretty close to reality. But philosophers and research advisers are there to warn us that the word is not the thing and that the model is not the reality.

And I think that is why some people mistakenly believe that numbers are "real". You can point at a number on a page but that's just ink that's been allowed to soak into paper and dry. To be grammatically correct, "1" is not 1. Fractions are even more problematic. If you break a stick in nature, you don't have two fractional sticks. You just have two sticks, and the "two" only exists in people's heads.

Mathematics is a language, just like English or Spanish or AMSLAN. It has been developed to help us come up with technically correct descriptions about how the world around us works.

In a way, numbers do have a kind of existence, as information, but that existence isn't independent. If there were no minds around to appreciate a zero, there would be no zero. But zero revolutionized our world by allowing us to make very precise "words" to describe very large and very small quantities.

Some machines have parts that must be accurate in size to ,say, 0.01 millimeters, or else the tiny space between the parts would allow enough motion to shake the machine apart. Try expressing 0.01 in Roman numerals (which have no zero).

Our technical understanding of the world, and therefore, our exquisite technology, relies on the language of mathematics, but language it still is.

We have many languages - literary language that allows us to communicate complex messages across both space and time, nonspoken body languages that allow us to communicate exquisitely our emotional intentions, aesthetic languages that let is communicate beauty (and sometimes ugliness)to multitudes. The sciences use the languages of logic and mathematics to communicate ideas with great precision.

Now, as I begin to explore the hard sciences, my first stop will be the "hard language" of mathematics and the softer human spoken languages.

Does mathematics exist "out there"? Well, in fact, it does. As long as there are thinking people "out there", there will be mathematics and I will be carrying it out into the field more and more to explore the intricacies of the world around me.

--- Hard science, soft science ---

"Hard" science is misleading. Social sciences, psychology, history - all that can be vastly more difficult than the "hard sciences". In the laboratory, everything other than what is being observed is controlled (and, often, what is being observed is also controlled, which begs the question, "Is what is being observed a fabrication?"). In the field, things can't be tightly controlled so there is always a lot of what scientists call "error".

"Error" isn't what it sounds like. It isn't "accident" or "misbehaving". The inconvenient fact is that even the purest of chemicals are not absolutely pure and there is no way of knowing exactly what impurities are present. No procedure is absolutely perfect and all we can do is specify how close to perfect it is (we can do that by specifying tolerances and checking to make sure these tolerances are met.)

Tiny imperfections are considered insignificant or negligible. Of course all the tiny imperfections add up, and that's what scientists call "error".

"Soft sciences" including field research in the hard sciences deal with lots of error so results of studies tend to include a lot of involved statistics that generate statements like, "The measurement is accurate within plus or minus ..... ," or "a trend was observed that ....," or "p is less than ...." These are statements of uncertainty.

In contrast, a hard scientist can confidentially tell you that the boiling point of pure water is 100.0 degree centigrade at one atmosphere of pressure. Observations made in the laboratory have very little error and therefore results of laboratory studies can often be reported with considerable certainty. Hard science is "hard" because of the "solidity" of it's results.

Up to now, I've been exploring the soft sciences around the Denver area, but I'm about to shift over to the hard sciences: mathematics, astronomy, physics, chemistry, geology, paleontology, biology. Along the way, you will see why even the hard sciences have their soft spots.