9.3: Path Independence
In Calculus I we had the Fundamental Theorem of Calculus that told us how to evaluate definite integrals. This told us,
It turns out that there is a version of this for line integrals over certain kinds of vector fields. Here it is.
Suppose that (C) is a smooth curve given by (vec rleft( t ight)), (a le t le b). Also suppose that (f) is a function whose gradient vector, ( abla f), is continuous on (C). Then,
Note that (vec rleft( a ight)) represents the initial point on (C) while (vec rleft( b ight)) represents the final point on (C). Also, we did not specify the number of variables for the function since it is really immaterial to the theorem. The theorem will hold regardless of the number of variables in the function.
This is a fairly straight forward proof.
For the purposes of the proof we’ll assume that we’re working in three dimensions, but it can be done in any dimension.
Let’s start by just computing the line integral.
Now, at this point we can use the Chain Rule to simplify the integrand as follows,
To finish this off we just need to use the Fundamental Theorem of Calculus for single integrals.
Let’s take a quick look at an example of using this theorem.
First let’s notice that we didn’t specify the path for getting from the first point to the second point. The reason for this is simple. The theorem above tells us that all we need are the initial and final points on the curve in order to evaluate this kind of line integral.
So, let (vec rleft( t ight)), (a le t le b) be any path that starts at (left( <1,frac<1><2>,2> ight)) and ends at (left( <2,1, - 1> ight)). Then,
[vec rleft( a ight) = leftlangle <1,frac<1><2>,2> ight angle hspace<0.5in>vec rleft( b ight) = leftlangle <2,1, - 1> ight angle ]
Notice that we also didn’t need the gradient vector to actually do this line integral. However, for the practice of finding gradient vectors here it is,
abla f = leftlangle < - pi sin left(
The most important idea to get from this example is not how to do the integral as that’s pretty simple, all we do is plug the final point and initial point into the function and subtract the two results. The important idea from this example (and hence about the Fundamental Theorem of Calculus) is that, for these kinds of line integrals, we didn’t really need to know the path to get the answer. In other words, we could use any path we want and we’ll always get the same results.
In the first section on line integrals (even though we weren’t looking at vector fields) we saw that often when we change the path we will change the value of the line integral. We now have a type of line integral for which we know that changing the path will NOT change the value of the line integral.
Let’s formalize this idea up a little. Here are some definitions. The first one we’ve already seen before, but it’s been a while and it’s important in this section so we’ll give it again. The remaining definitions are new.
First suppose that (vec F) is a continuous vector field in some domain (D).
- (vec F) is a conservative vector field if there is a function (f) such that (vec F =
abla f). The function (f) is called a potential function for the vector field. We first saw this definition in the first section of this chapter.
A path (C) is called closed if its initial and final points are the same point. For example, a circle is a closed path.
A path (C) is simple if it doesn’t cross itself. A circle is a simple curve while a figure 8 type curve is not simple.
A region (D) is open if it doesn’t contain any of its boundary points.
With these definitions we can now give some nice facts.
This is easy enough to prove since all we need to do is look at the theorem above. The theorem tells us that in order to evaluate this integral all we need are the initial and final points of the curve. This in turn tells us that the line integral must be independent of path.
This fact is also easy enough to prove. If (vec F) is conservative then it has a potential function, (f), and so the line integral becomes ( displaystyle intlimits_ These are some nice facts to remember as we work with line integrals over vector fields. Also notice that 2 & 3 and 4 & 5 are converses of each other. From central Aspen (Hotel Jerome), drive Highway 82 (Independence Pass Road) 15 miles. For parking you'll find a wide shoulder on the right side of the road, where Green Mountain's visible northerly faces rise to the southwest from across the flats of the Roaring Fork drainage. From the east, drive over Independence Pass and park about 5 miles down from the pass summit. Note that Green Mountain is actually a 4-mile-long summit-studded ridge, with many ski and snowboard routes thus, this trailhead only functions for one part of the ridge. Trailhead variations are covered in the route descriptions. In our experience here at backcountryskiingco.com, finding these trailheads is quite simple so long as you pay attention to your odometer and look up to the south when you get close to your chosen routes. Independence Townsite Trailhead If you're coming from the Aspen direction (driving E), you'll find this trailhead 16 miles from central Aspen (Hotel Jerome). If you're driving W, head over Independence Pass 4 miles. Park in an obvious parking area (10,920 feet) on the south side of the road, above a group of old buildings (the historic Independence ghost town). Map below is a Flash file and may not display on some devices. If not, perhaps you can use our backcountryskiingco.com PDF version. Climb rating: Harder skins, Intermediate snow climbing Ski rating: Advanced, S4 Recommended seasons: Spring snow Starting elevation: 10,220 feet Summit elevation: 12,791 feet Elevation gain: 2,571 feet Round trip distance: 3 miles Day trip? Yes Map: Lower Independence Photo: [in collection] Green Mountain is a huge ridge running 4 miles from the Lincoln Creek and Roaring Fork confluence (see sections above) all the way to Independence Mountain above the town of Independence (see routes below). This route takes the true summit, which is located some distance west of where most people ski. Note that the trailhead described here is not that described in the section introduction. From central Aspen (Hotel Jerome), drive 12.4 miles up Independence Pass Road. If you're driving W, head over Independence Pass and park 8 miles down from the pass summit. To help find the trailhead, calibrate your altimeter to 7,900 feet in Aspen, or to 12,090 feet atop Independence Pass. Your exact parking and starting point is on the road shoulder (10,220 feet) next to a huge avalanche path which you can look up to a point near the summit of Green Mountain. Do not mistake this slide for a similar one .6 miles closer to Aspen. Climb the avalanche path, which becomes a shoulder leading S to Green Mountain's summit. Descend your ascent route with variations you eyed on the ascent. Interesting steep bowls drop from the ridge both east and west of the summit. An extension ladder can be used for the stream crossing.
Upper Indy Southern -- Chap. 9 Section 3
Route 9.3.1 Green Mountain Summit Direct via Avalanche Path
Avalanche path leading from HWY 82 to Green Mountain Summit, good spring skiing if consolidated and safe, but stay off if any avalanche danger. Several close calls here over the years. Photo, BackcountrySkiingCO.com
These are some nice facts to remember as we work with line integrals over vector fields. Also notice that 2 & 3 and 4 & 5 are converses of each other.
From central Aspen (Hotel Jerome), drive Highway 82 (Independence Pass Road) 15 miles. For parking you'll find a wide shoulder on the right side of the road, where Green Mountain's visible northerly faces rise to the southwest from across the flats of the Roaring Fork drainage. From the east, drive over Independence Pass and park about 5 miles down from the pass summit. Note that Green Mountain is actually a 4-mile-long summit-studded ridge, with many ski and snowboard routes thus, this trailhead only functions for one part of the ridge. Trailhead variations are covered in the route descriptions. In our experience here at backcountryskiingco.com, finding these trailheads is quite simple so long as you pay attention to your odometer and look up to the south when you get close to your chosen routes.
Independence Townsite Trailhead
If you're coming from the Aspen direction (driving E), you'll find this trailhead 16 miles from central Aspen (Hotel Jerome). If you're driving W, head over Independence Pass 4 miles. Park in an obvious parking area (10,920 feet) on the south side of the road, above a group of old buildings (the historic Independence ghost town).
Map below is a Flash file and may not display on some devices. If not, perhaps you can use our backcountryskiingco.com PDF version.
Climb rating: Harder skins, Intermediate snow climbing Ski rating: Advanced, S4 Recommended seasons: Spring snow Starting elevation: 10,220 feet Summit elevation: 12,791 feet Elevation gain: 2,571 feet Round trip distance: 3 miles Day trip? Yes Map: Lower Independence Photo: [in collection]
Green Mountain is a huge ridge running 4 miles from the Lincoln Creek and Roaring Fork confluence (see sections above) all the way to Independence Mountain above the town of Independence (see routes below). This route takes the true summit, which is located some distance west of where most people ski. Note that the trailhead described here is not that described in the section introduction.
From central Aspen (Hotel Jerome), drive 12.4 miles up Independence Pass Road. If you're driving W, head over Independence Pass and park 8 miles down from the pass summit. To help find the trailhead, calibrate your altimeter to 7,900 feet in Aspen, or to 12,090 feet atop Independence Pass. Your exact parking and starting point is on the road shoulder (10,220 feet) next to a huge avalanche path which you can look up to a point near the summit of Green Mountain. Do not mistake this slide for a similar one .6 miles closer to Aspen. Climb the avalanche path, which becomes a shoulder leading S to Green Mountain's summit. Descend your ascent route with variations you eyed on the ascent. Interesting steep bowls drop from the ridge both east and west of the summit. An extension ladder can be used for the stream crossing.
Route 9.3.2 Green Mountain Glades to Green Mountain Summit
Climb rating: Moderate skins, easy boots. Ski rating: Intermediate, S3. Recommended seasons: Spring snow or early winter Starting elevation: 10,720 feet Summit elevation: 12,791 feet Elevation gain: 2,100 feet Round trip distance: 4 miles Day trip? Yes Maps: Lower Independence, Independence North
This is the easiest ski on Green Mountain and a good learner's tour, but due to trees and sun exposure, it may go out of condition quickly in spring. (With snowmobile access via the Independence Pass road, this might be a good place for winter powder.) Drive to Upper Green Mountain Trailhead (as described in the section introduction). When you end up on the road next to Green Mountain you'll notice that most of Green Mountain is a long ridge broken by a ribs, shoulders and avalanche paths, with one wooded shoulder dropping to the valley at the westerly end of the terrain you're studying. This is the first part of your destination.
But the crux of this route (and others on Green's north face) is crossing the Roaring Fork River. The authors here at backcountryskiingco.com have done everything from wading with tennis shoes to bringing an extension ladder and laying it across a narrower channel. Snow bridges may exist during heavy snow years, and long-legged people can sometimes find a jump route. Fishing waders are another option. Whatever your method, after you cross the creek, head up the glades and open areas. Use an old mining road when appropriate. Trend right (W) and continue to timberline. Once above timberline you can climb directly to the ridge above, or take a climbing traverse W at about 11,900 feet to reach a large saddle (12,000 feet). From here head up an attractive low-angled snow shoulder to one of Green Mountain's summits (12,690 feet). If you want the real top, take the ridge from here W and S to the highpoint (12,791 feet). Descend your ascent route.
|Green Mountain routes, northeast side, from HWY 82. Click image to enlarge.|
Route 9.3.3 Green Mountain Northeast Face
Climb rating: Harder skins, easy boots Ski rating: Advanced, S3 Recommended seasons: Spring snow Starting elevation: 10,780 feet Summit elevation: 12,395 feet Elevation gain: 1,615 feet Round trip distance: 2 miles Day trip? Yes Map: Independence North
The northerly side of Green Mountain ridge dropping to Independence Pass Road offers innumerable possibilities. If you're new to the area you can get oriented by first going to the Independence Townsite Trailhead (section introduction) and from there identifying Independence Mountain (12,703 feet , see routes below elevation?). As you drive a mile from there down the road to Upper Green Mountain Trailhead (see section introduction), refer to a map and identify each Green Mountain summit.
A common route takes the distinct avalanche path just east (climber's left) of the western glades mentioned above as route 9.3.2?. Drive to the Upper Green Mountain Trailhead as described in the section introduction. From parking beside the pavement, you'll look southwest up the route, which leads to a saddle between two summits. Climb to the saddle, then take the ridge to either summit (or for a quickie forget the summits and stop at the saddle). Drop your ascent route. Remember the terrain in this area is only safe during times of lowest avalanche hazard, most often during the morning with a compacted spring snowpack.
|More Green Mountain options as viewed from HWY 82, these can be quick hits, but the stream crossing may be difficult. If neccesary, cross stream farther upvalley, possibly using an extension ladder. Click image to enlarge.|
Route 9.3.4 Independence Mountain
Climb rating: Harder skins, Easy boots Ski rating: Advanced, S3 Recommended seasons: Spring snow Starting elevation: 10,840 feet Summit elevation: 12,703 feet Elevation gain: 1,863 feet Round trip distance: 4 miles Day trip? Yes Maps: Independence North, Independence South Photo: [several in collection show this]
This classic takes the fine-looking mountain rising south of the Independence ghost town. Drive to Independence Townsite Trailhead, look south, and you can't miss it. If you know what you're looking at, you also get a good view of Independence Mountain from the road near Independence Pass summit. Head down through the townsite cabins and cross the Roaring Fork River (may require wading). The simplest route starts in the small gulch containing Independence Creek, then climbs an avalanche path up the peak's north shoulder. This funnels you up to the north ridge, which you can take to the summit. You can glisse your ascent route or take the popular east bowl (might be slightly easier skiing). Both come highly recommended.
Route 9.3.5 Independence Mountain-North Face
Climb rating: Harder skins, Easy boots Ski rating: Extreme, S4+ Recommended seasons: Spring snow Starting elevation: 10,840 feet Summit elevation: 12,703 feet Elevation gain: 1,863 feet Round trip distance: 4 miles Day trip? Yes Maps: Independence North, Independence South Photo: [in collection]
For the extremist's line on Independence Mountain, the obvious north face is a good bet. Start from Independence Townsite Trailhead, and climb Independence Mountain via route 9.2.4 or by the north face. You know what comes next. The best line takes the center of the face it's not as steep as it looks from the road, but it'll keep you honest. Other lines are available.
Route 9.3.6 Heart Attack Hill
Climb rating: Easy skins or boots Ski rating: S2 Recommended seasons: All with snowcover Starting elevation: 12,000 feet Summit elevation: 12,560 feet Elevation gain: 560 feet Round trip distance: 1 mile Day trip? Yes Map: Independence North Photo: [several in collection show this]
Finally, one of those legendary easy routes. But watch your heart. Nothing like being flabby and trying to climb at 12,000 feet -- you will feel it. This excellent little hill is located about ½ mile down the road west from the Independence Pass Summit (see section introduction). If the road shoulder is packed, park at the base the hill (keep tires well away from pavement or risk a ticket). If parking is limited, park at the pass summit and scoot E and SE up the broad slopes. The top of Heart Attack Hill is a nondescript flat area (12,560 feet) with a good view. Indeed, if you're new to the pass do this short jaunt as a familiarization tour. Repeat laps for more vertical. This is a good place for children, but watch the actual fall line which can suck the unwary (or immature) down W into dangerous steep terrain above the Roaring Fork River.
There is a large area of low-angled terrain (S1) between Heart Attack Hill and the pass summit: a good place for beginners or raging skate skiers.
|Independence Pass summit area viewed from east. Click image to enlarge.|
Route 9.3.7 Snow Fence Ridge and Mountain Boy Gulch
Climb rating: Easy skins, easy boots Ski rating: S4- Recommended seasons: Spring snow season Starting elevation: 12,000 feet Summit elevation: 12,812 feet Elevation gain: 812 feet Trip distance: 3 miles Day trip? Yes Maps: Independence North, Independence South Photo: [several in collection show this route]
You'll see a lot of tracks on this route, partly because it's one of those gifts that yields more downhill than uphill by using piston travel, but also because it's simply a great place to ski or snowboard. Follow route 9.3.6 to Heart Attack Hill. Continue across a flat area then up the prominent ridge about a mile to a bump on the ridge known as Snow Fence Peak (12,812 feet). A broad shoulder known as The Nose drops east from the summit and is usually accessed via a short cornice drop. The shoulder leads to a low-angled area. Head to skier's left here (N), and then pick your way E down through steeper terrain into Mountain Boy Gulch. This steeper section can present unexpected avalanche danger in spring if you're there after a warm night, since parts of the snowpack will be poorly bonded to rock slabs. If you're worried about the steeps, here at backcountryskiingco.com we recommend circling to skier's right for lower angled terrain. Once in the drain, take Mountain Boy Gulch down to a hairpin turn (11,500 feet) on Independence Pass Road. Catch a ride or use your stashed vehicle. It's traditional for anyone with a vehicle here to load as many skiers as possible for the shuttle back up the road. Remember the golden rule.
Snow Fence Ridge is named after the Rube Goldberg structures built on the ridge in the 1960s intended to change the patterns of snow deposition so that more snowmelt would flow to the Eastern Slope. Most of the fences have been removed, but dangerous metal stakes can catch the unwary glisser.
|Looking southeast from Independence Pass, Mountain Boy area. Click image to enlarge.|
Route 9.3.8 Mountain Boy Peak
Climb rating: Moderate skins, easy boots Ski rating: S4- Recommended seasons: Spring snow Starting elevation: 12,000 feet Summit elevation: 13,198 feet Elevation gain: about 1,500 feet, depends on exact route Round trip distance: about 5 miles, depends on exact route Day trip? Yes Maps: Independence North, Independence South Photo: [in collection]
It's only the 489th highest mountain in Colorado, but Mountain Boy Peak is worth your time. You can get to this peak via a simple southerly traverse from Heart Attack Hill for about 2 miles S on Snow Fence Ridge (route 9.3.7) . That choice is scenic, but you do a lot of walking for the downhill you finally get. If you want more glisse, go to the Snow Fence Ridge summit and ski into Mountain Boy Gulch. After enjoying turns down to about 12,200 feet, slap your skins back on and climb through Mountain Boy Park Basin S then SW to the obvious saddle at the head of the basin, to the right of Mountain Boy's summit. As you tour, you'll see an attractive couloir dropping from an intermediary point on the ridge. This is known as the Cosmic Couloir, which must be a joke because it's fun to glisse, not that steep, and equals about one percent of such awesome drops as Grizzly Peak. But, if you insist, make a cosmic bonus run.
At any rate, once you're back to the ridge, follow it to Mountain Boy Peak's summit. From the summit, for a shorty you can ski a couloir at skier's left on the north face (which you doubtless saw on the way up the basin). If you have the energy, descend the east face from the summit into a classic basin. Enjoy turns to about 11,800 feet. Put your skins on yet again, and climb N to a saddle, then W to the summit of what's fondly known as Mountain Boy Hill (at least you'll know it as that by now.) From Mountain Boy Hill, ski down low-angled slopes E, then swing N, continuing down into Mountain Boy Gulch. If you stick to it, you'll ski to within a few hundred yards of a hairpin switchback on Independence Pass Road (11,500 feet). Catch a ride back to the pass, or use the vehicle you stashed there because of your with worthy foresight.
Route 9.3.9 Fourth of July Bowls
Climb rating: Easy skins or boots Ski rating: S4- Recommended seasons: Spring snow Starting elevation: 12,000 feet Summit elevation: 12,480 feet Elevation gain: 480 feet Trip distance: 2 miles Day trip? Yes Map: Independence North Photo: [in collection]
This area gets skied and ridden so much it's practically a resort with no lifts. Moguls have even been spotted at some of the narrow egress points! Okay, you do get about 1,500 vertical of skiing for only 480 of climbing, so perhaps the moguls are worth it. Before you glisse, familiarize yourself with Fourth of July by driving past the base of the run via Independence Pass Road. If you're coming from Aspen, spot the Independence ghost town at about 16 miles from town. As you continue driving past the ghost town, Fourth of July is the series of attractive bowls and shoulders you'll see up to your right (south). There are scores of descents.
For your first trip down Fourth of July, the main bowl is a good bet. Start by climbing most of the way up Heart Attack Hill ( elevation or route 9.3.6 ?). Traverse SW around the top of the hill (just a few feet below the actual summit), and cross a broad saddle. You're now at the start of Snow Fence Ridge (9.3.7. ). Instead of climbing the ridge, continue contouring SW from the saddle. After a few hundred yards you'll be at the rim of Fourth of July Bowl. Nail it.
Variations from this point take a broad shoulder to rider's left of the bowl. Or farther west, you can drop a beautiful avalanche path down to the river and road. Crossing the river can be problematic. Look for snow bridges in early spring. You can rock hop in a few places, but you'll have to wade if the river is fully spating. Over the years, skiers have built makeshift bridges with planks they hauled up the road and carried down to the stream. If you're fortunate you'll find one. Have a car stashed on the road, or beg a ride.
This area is called Fourth of July because the town of Independence was founded July 4, 1879, and because the bowl is sometimes skiable in July, or at least it is for fanatics such as those of us here at backcountryskiingco.com!
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The information presented within this website is based upon the experience of the authors and their sources and might not necessarily be perceived as accurate by other persons therefore, extreme care should be taken when following any of the routes described here. This website is not intended to be instructional in nature but rather a guide for mountaineers who already have the requisite training, experience and knowledge. An advanced level of expertise and physical conditioning is necessary for even the "easiest" of the routes described. Proper clothing and equipment are essential. Failure to have the necessary knowledge, equipment, and conditioning will subject you to extreme physical danger, injury, or death. Some routes have changed and others will change avalanche hazards may have expanded or new hazards may have formed since this website's publication. Moreover, this website does not list every hazard you may encounter. One element of the beauty, freedom, and excitement of wilderness is the presence of risks that do not confront us in civilization. When you travel in the backcountry you assume those risks. They can be met with reasonable safety, but only if you exercise independent judgment and common sense.
America's path to energy independence in 2 charts
The share of oil consumed by Americans that was produced in the US has sharply increased over the last 10 years, as you can see in this chart shared by Mark J. Perry of the American Enterprise Institute .
Back in 2005, less than 70% of oil consumed by Americans was produced by US oil.
But thanks to developments in the hydraulic fracturing technology, that number's now up to a whopping 89%.
That would be the highest level of energy-self efficiency since 1984.
Additionally, net imports have also been tumbling over the years. Back in 2005, the number was above 60%, but today net oil imports are only 25.2% — the lowest level of net petroleum imports since 1971, Perry notes.
Recently, the Energy Information Administration said in its new survey-based output data that the US was pumping out just below 9.3 million barrels per day in June, slightly below May's output . By comparison, Saudi Arabia's pum ped about 9.51 million barrels per day in May, down from March's peak of 9.69 million per day.
"The Great American Shale Boom continues to set new production records and reach new milestones on a regular basis and has turned out to be the most dynamic, successful, and powerful single sector of the US economy, thanks to the 'American-made' drilling technologies pioneered and developed by America's 'petropreneurs,'" Perry noted last year.
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Coinciding with other 1960s and 1970s indigenous activist movements, the Hawaiian sovereignty movement was spearheaded by Native Hawaiian activist organizations and individuals who were critical of issues affecting modern Hawaii, including urbanization and commercial development of the islands, corruption in the Hawaiian Homelands program, and the appropriation of native burial grounds and other sacred spaces.  During the 1980s, the movement gained cultural and political traction and native resistance grew in response to urbanization and native disenfranchisement. Local and federal legislation provided some protection for native communities but did little to quell expanding commercial development. 
In 1993, a joint congressional resolution apologized for the 1893 overthrow of the Hawaiian monarchy, and said that the overthrow was illegal.   In 2010, the Akaka Bill passed, which provided a process for US federal recognition of Native Hawaiians and gave ethnic Hawaiians some control over land and natural resource negotiations. However, the bill was opposed by sovereignty groups because of its provisions that legitimized illegal land transfers, and was criticized by a 2006 U.S. Commission on Civil Rights report (which was later reversed in 2018)  for the effect it would have on non-ethnic Hawaiian populations.  A 2005 Grassroot Institute poll found the majority of Hawaiian residents opposed the Akaka Bill. 
The ancestors of Native Hawaiians may have arrived in the Hawaiian Islands around 350 CE, from other areas of Polynesia.  By the time Captain Cook arrived, Hawaii had a well-established culture with a population estimated to be between 400,000 and 900,000 people.  Starting in 1795 and completed by 1810, Kamehameha I conquered the entire archipelago and formed the unified Kingdom of Hawaii. In the first one hundred years of contact with Western civilization, due to disease and war, the Hawaiian population dropped by ninety percent, to only 53,900 people in 1876.  American missionaries would arrive in 1820 and assume great power and influence.  Despite formal recognition of the Kingdom of Hawaii by the United States  and other world powers, the kingdom was overthrown beginning January 17, 1893, with a coup d'état orchestrated by, mostly, Americans within the kingdom's legislature, with aid from the United States military.  
The Blount Report is the popular name given to the part of the 1893 United States House of Representatives Foreign Relations Committee Report regarding the overthrow of the Kingdom of Hawaii. The report was conducted by U.S. Commissioner James H. Blount, appointed by U.S. President Grover Cleveland to investigate the events surrounding the January 1893 coup. This report provides the first evidence that officially identifies the United States' complicity in the overthrow of the government of the Kingdom of Hawaii.  Blount concluded that U.S. Minister to Hawaii John L. Stevens had, in fact, carried out unauthorized partisan activities that included the landing of U.S. Marines under a false or exaggerated pretext to support anti-royalist conspirators the report went on to find that these actions were instrumental to the success of the revolution and that the revolution was carried out against the wishes of a majority of the population of the Hawaiian Kingdom and/or its Royalty. 
On December 14, 1893, Albert Willis arrived unannounced in Honolulu aboard the USRC Corwin, bringing with him an anticipation of an American invasion in order to restore the monarchy, which became known as the Black Week. Willis was the successor to James Blount as United States Minister to Hawaii. With the hysteria of a military assault, he staged a mock invasion with the USS Adams and USS Philadelphia, directing their guns toward the capital. He also ordered rear admiral John Irwin to organize a landing operation using troops on the two American ships, which were joined by the Japanese Naniwa and the British HMS Champion. On January 11, 1894, Willis revealed the invasion to be a hoax.   After the arrival of the Corwin, the provisional government and citizens of Hawaii were ready to rush to arms if necessary, but it was widely believed that Willis' threat of force was a bluff.  
On December 16, the British Minister to Hawaii was given permission to land marines from HMS Champion for the protection of British interests the ship's captain predicted that the Queen and Sovereign ruler (Liliuokalani) would be restored by the U.S. military.   In a November 1893 meeting with Willis, Liliuokalani indicated that she wanted the revolutionaries punished and their property confiscated, despite Willis' desire for her to grant amnesty to her enemies.  In a December 19, 1893, meeting with the leaders of the provisional government, Willis presented a letter written by Liliuokalani, in which she agreed to grant amnesty to the revolutionaries if she was restored as queen. During the conference, Willis told the provisional government to surrender to Liliuokalani and allow Hawaii to return to its previous condition, but the leader of the provisional government, President Sanford Dole, refused to comply with his demands, claiming that he was not subject to the authority of the United States.   
The Blount Report was followed in 1894 by the Morgan Report, which contradicted Blount's report by concluding that all participants except for Queen Lili'uokalani were "not guilty".  : 648 U.S. Secretary of State Walter Q. Gresham announced on January 10, 1894, that the settlement of the situation in Hawaii would be left up to Congress, following Willis' unsatisfactory progress. Cleveland said that Willis had carried out the letter of his directions, rather than their spirit.  Domestic response to Willis' and Cleveland's efforts was largely negative. The New York Herald wrote, "If Minister Willis has not already been ordered to quit meddling in Hawaiian affairs and mind his own business, no time should be lost in giving him emphatic instructions to that effect." The Democratic New York World wrote: "Is it not high time to stop the business of interference with the domestic affairs of foreign nations? Hawaii is 2000 miles from our nearest coast. Let it alone." The Democratic New York Sun said: "Mr. Cleveland lacks . the first essential qualification of a referee or arbitrator." The Republican New York Tribune called Willis' trip a "forlorn and humiliating failure to carry out Mr. Cleveland's outrageous project." The Republican New York Recorder wrote, "The idea of sending out a minister accredited to the President of a new republic, having him present his credentials to that President and address him as 'Great and Good Friend,' and then deliberately set to work to organize a conspiracy to overthrow his Government and re-establish the authority of the deposed Queen, is repugnant to every man who holds American honor and justice in any sort of respect." The Democratic New York Times was one of the few New York newspapers that defended Cleveland's decisions, saying that "Mr. Willis discharged his duty as he understood it." 
Following the overthrow, in 1894 the Provisional Government of Hawaii became the Republic of Hawaii, and in 1898 the Republic of Hawaii was annexed by the United States in the Newlands Resolution, becoming the Territory of Hawaii.   The territory was then given a territorial government in an Organic Act in 1900. While there was much opposition to the overthrow of the Kingdom of Hawaii and many attempts to restore the kingdom, it became a territory of the US in 1898, without any input from Native Hawaiians.  Hawaii became a US state on March 18, 1959, following a referendum in which at least 93% of voters approved of statehood. By then, most voters were not Native Hawaiian. The 1959 referendum did not have an option for independence from the United States. Following Hawaii's admission as a state, the United Nations removed Hawaii from its list of non-self-governing territories (a list of territories that are subject to the decolonization process). 
The US constitution recognizes Native American tribes as domestic, dependent nations with inherent rights of self-determination through the US government as a trust responsibility, which was extended to include Eskimos, Aleuts and Native Alaskans with the passing of the Alaska Native Claims Settlement Act. Through enactment of 183 federal laws over 90 years, the US has entered into an implicit—rather than explicit—trust relationship that does not give formal recognition of a sovereign people having the right of self-determination. Without an explicit law, Native Hawaiians may not be eligible for entitlements, funds and benefits afforded to other US indigenous peoples.  Native Hawaiians are recognized by the US government through legislation with a unique status.  Proposals have been made to treat Native Hawaiians as a tribe similar to Native Americans opponents to the tribal approach argue that it is not a legitimate path to nationhood. 
New Jersey Department of Education
New: The New Jersey Student Learning Standards (NJSLS) are reviewed and revised every five years. The 2020 NJSLS were adopted by the State Board of Education on June 3, 2020. The 2020 New Jersey Student Learning Standards webpage provides links to the 2020 NJSLS and information regarding curriculum implementation dates.
In today's global economy, students need to be lifelong learners who have the knowledge and skills to adapt to an evolving workplace and world. To address these demands, Standard 9, 21st Century Life and Careers, which includes the 12 Career Ready Practices, establishes clear guidelines for what students need to know and be able to do in order to be successful in their future careers and to achieve financial independence.
Mission: 21st century life and career skills enable students to make informed decisions that prepare them to engage as active citizens in a dynamic global society and to successfully meet the challenges and opportunities of the 21st century global workplace.
Vision: To integrate 21st Century life and career skills across the K-12 curriculum and in Career and Technical Education (CTE) programs to foster a population that:
- Continually self-reflects and seeks to improve the essential life and career practices that lead to success.
- Uses effective communication and collaboration skills and resources to interact with a global society.
- Is financially literate and financially responsible at home and in the broader community.
- Is knowledgeable about careers and can plan, execute, and alter career goals in response to changing societal and economic conditions.
- Seeks to attain skill and content mastery to achieve success in a chosen career path.
The Standards: Standard 9 is composed of the Career Ready Practices and Standard 9.1, 9.2, and 9.3 which are outlined below:
- The 12 Career Ready Practices
These practices outline the skills that all individuals need to have to truly be adaptable, reflective, and proactive in life and careers. These are researched practices that are essential to career readiness.
- 9.1 Personal Financial Literacy
This standard outlines the important fiscal knowledge, habits, and skills that must be mastered in order for students to make informed decisions about personal finance. Financial literacy is an integral component of a student's college and career readiness, enabling students to achieve fulfilling, financially-secure, and successful careers.
- 9.2 Career Awareness, Exploration, and Preparation
This standard outlines the importance of being knowledgeable about one's interests and talents, and being well informed about postsecondary and career options, career planning, and career requirements.
- 9.3 Career and Technical Education
This standard outlines what students should know and be able to do upon completion of a CTE Program of Study.
For students to be college and career ready they must have opportunities to understand career concepts and financial literacy. This includes helping students make informed decisions about their future personal, educational, work, and financial goals. By integrating Standard 9 into instruction, New Jersey students will acquire the necessary academic and life skills to not only achieve individual success but also to contribute to the success of our society.
American School Counselor Association, A. S. (2004). ASCA National Standards for Students (Competencies and Indicators). Alexandria, VA.
Career Readiness Partner Council. (2014). What it Means to be Career Ready? https://cte.careertech.org/sites/default/files/CRPC_4pager.pdf
Advance CTE: State Leaders Connecting Learning to Work. (2014, June) The Common Career Technical Core. https://www.careertech.org/cctc
Folkers, D. R. (2011, October). Setting a New Standard with a Common Career Technical Core. Techniques.
Partnership for 21st Century Skills. http://www.p21.org/
Copyright © State of New Jersey, 1996 - 2019
NJ Department of Education, PO Box 500, Trenton, NJ 08625-0500, (609) 376-3500
On its 73rd Independence Day, Israel’s population hits 9.3 million
(April 15, 2021 / JNS) Ahead of Israel’s 72nd Independence Day, the Central Bureau of Statistics (CBS) has published the nation’s latest population figures.
The Jewish state is home to 9,327,000 people, among them 6.894 million Jews (73.9 percent of the population), 1.966 million Arabs (21.1 percent) and 467,000 citizens of other ethnicities (5 percent).
Demographic growth projections indicate that in 2030, Israel’s population will stand at 11.1 million, and in 2040 at 13.2 million. By the time Israel marks its 100th Independence Day in 2048, its population is projected to be 15.2 million.
The state has a young population with 28.1 percent of Israelis being between the age of 0 and 14, and only 12 percent being over 65.
CBS data shows that at the end of 2019, a total of 46 percent of Jews in the world lived in Israel and that 78 percent of the Jews in Israel were born in the country.
When the state was founded, its population stood at 806,000 with 82.1 percent of the population being Jewish and 17.9 percent Arab. Since 1948, 3.3 million immigrants have arrived, 44.7 percent of whom made aliyah in 1990 or later.
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Independence Day, also called Fourth of July or July 4th, in the United States, the annual celebration of nationhood. It commemorates the passage of the Declaration of Independence by the Continental Congress on July 4, 1776. Independence Day is celebrated on Sunday, July 4, 2021 in the United States.
When is Independence Day in the United States?
Independence Day is celebrated in the United States on July 4. Often the holiday is called the Fourth of July.
What is the Fourth of July?
The Fourth of July celebrates the passage of the Declaration of Independence by the Continental Congress on July 4, 1776. The Declaration announced the political separation of the 13 North American colonies from Great Britain.
Why is the Fourth of July celebrated with fireworks?
In Fourth of July celebrations, fireworks signify national pride and patriotism. They had been used in China since at least the 12th century, and in the 15th century they became popular with European monarchs as a way to celebrate national triumphs, the restoration of peace, and the monarchs’ own birthdays. Fireworks have been part of Independence Day in the United States since its first celebration, in 1777.
Why did the North American colonies declare independence?
The Declaration of Independence, passed on July 4, 1776, reflected widespread dissatisfaction in the colonies with increased British control. Colonists especially opposed a series of unpopular laws and taxes enacted by Britain beginning in 1764, including the Sugar Act, the Stamp Act, and the so-called Intolerable Acts.
The Congress had voted in favour of independence from Great Britain on July 2 but did not actually complete the process of revising the Declaration of Independence, originally drafted by Thomas Jefferson in consultation with fellow committee members John Adams, Benjamin Franklin, Roger Sherman, and William Livingston, until two days later. The celebration was initially modeled on that of the king’s birthday, which had been marked annually by bell ringing, bonfires, solemn processions, and oratory. Such festivals had long played a significant role in the Anglo-American political tradition. Especially in the 17th and 18th centuries, when dynastic and religious controversies racked the British Empire (and much of the rest of Europe), the choice of which anniversaries of historic events were celebrated and which were lamented had clear political meanings. The ritual of toasting the king and other patriot-heroes—or of criticizing them—became an informal kind of political speech, further formalized in mid-18th century when the toasts given at taverns and banquets began to be reprinted in newspapers.
In the early stages of the revolutionary movement in the colonies during the 1760s and early ’70s, patriots used such celebrations to proclaim their resistance to Parliament’s legislation while lauding King George III as the real defender of English liberties. However, the marking of the first days of independence during the summer of 1776 actually took the form in many towns of a mock funeral for the king, whose “death” symbolized the end of monarchy and tyranny and the rebirth of liberty.
During the early years of the republic, Independence Day was commemorated with parades, oratory, and toasting in ceremonies that celebrated the existence of the new nation. These rites played an equally important role in the evolving federal political system. With the rise of informal political parties, they provided venues for leaders and constituents to tie local and national contests to independence and the issues facing the national polity. By the mid-1790s the two nascent political parties held separate partisan Independence Day festivals in most larger towns. Perhaps for this reason, Independence Day became the model for a series of (often short-lived) celebrations that sometimes contained more explicit political resonance, such as George Washington’s birthday and the anniversary of Jefferson’s inauguration while he served as president (1801–09).
The bombastic torrent of words that characterized Independence Day during the 19th century made it both a serious occasion and one sometimes open to ridicule—like the increasingly popular and democratic political process itself in that period. With the growth and diversification of American society, the Fourth of July commemoration became a patriotic tradition which many groups—not just political parties—sought to claim. Abolitionists, women’s rights advocates, the temperance movement, and opponents of immigration (nativists) all seized the day and its observance, in the process often declaring that they could not celebrate with the entire community while an un-American perversion of their rights prevailed.
With the rise of leisure, the Fourth of July emerged as a major midsummer holiday. The prevalence of heavy drinking and the many injuries caused by setting off fireworks prompted reformers of the late 19th and the early 20th century to mount a Safe and Sane Fourth of July movement. During the later 20th century, although it remained a national holiday marked by parades, concerts of patriotic music, and fireworks displays, Independence Day declined in importance as a venue for politics. It remains a potent symbol of national power and of specifically American qualities—even the freedom to stay at home and barbecue.