BigLar

This seems to imply differentiability, too, although there are pathological function that are continuous everywhere but differentiable nowhere.

JS

Nope, differentiable means the first derivative is continuous.

Consider y=abs(x). It is continuous at every point, including the sharp point at x=0 (left limit = right limit = 0). It is differentiable at every point except x=0, because the derivative from the left is -1 and the derivative from the right is +1.

The first derivative of y=abs(x) is -1 up to x=0 and then suddenly jumps to +1 for x>0, and that is not continuous.


[This message has been edited by JS (edited 06-30-2003).]

LastClass

Uh, people? I had a different definition of "straight" in mind.

Canarsie

Thank you for the corrections, JS. Me, an “expert” Hardly!

Just what we need: a couple of roads scholars...

swag

Speaking of continuous, will they ever connect I-95 in NJ???

I have personally run afoul of this. Back in my college days, I was driving from NYC to Philly. I knew the NJ Turnpike was I-95, and looked at a map of Philly and saw I-95 went right thru downtown. No problemo, easy drive, right? No way I could miss downtown Philly...

So I head south on the Turnpike. When I passed a sign that said "Welcome to Delaware", I figured something wasn't quite right...

[This message has been edited by swag (edited 06-30-2003).]

LIH Prem

I know .. I just kill myself sometimes.

Canarsie

Thank you for bringing up something that has been a sore point with me also, swag.

Officially, Interstate 95 ends at exit 10 on the New Jersey Turnpike (with the interchange with Interstate 287/New Jersey 440) and does not begin again until some bizarre random point north of Trenton (not even at a designated exit!) where Interstate 295 northbound all of a sudden miraculously becomes Interstate 95 southbound. Technically, Interstate 95 has never been completed. New Jersey has the only incomplete section of Interstate 95 and — as far as I know — there are no plans anytime soon to complete it. The New Jersey Turnpike Authority, based in East Brunswick just off of exit 9, has an abundnce of political clout in New Jersey and is thought to be the major “road block” to the completion of Interstate 95. If Interstate 95 was ever completed, that would mean lost revenue for the New Jersey Turnpike, whose executives “earn” six-figure salaries. This was a bone of contention when radio station New Jersey 101.5 launched a grass-roots public campaign 10 years ago (and failed as the campaign whimpered a slow, quiet death) to abolish the tolls on New Jersey’s roadways.

If you have driven down the New Jersey Turnpike, not only is access to the Pennsylvania section Interstate 95 so restricted that it is not worth the effort, but it is also difficult to access Interstate 295, which is parallel to the New Jersey Turnpike in southern New Jersey. One will not see road signs to either road, except “To Interstate 95”, which will lead you to — you guessed it — Delaware.

More information about the New Jersey Turnpike can be found here.

Canarsie

Here is a Top 10 list of America's Most and Least Drivable Cities in 2003, for those who are interested.

LIH Prem

I guess Kauai and the other outer islands of Hawaii aren't part of the nation according to the authors.

-David

pdhenry

The discussion of the I-95 issues in NJ reminded me of another interesting observation -

Ever notice that the PA Turnpike never (almost never) intersects directly with any of the interstates that it crosses? Usually there are exits close enough that making a transition is reasonably possible, but try going from I-95 to the Turnpike NE of Philadelphia. The signs on the two roads don't even imply that such a thing is possible.

And even where the interchange is facilitated, the traffic is gnerally a mess - look at the intersection at I-70 in Breezewood, for example.

The story as I understand it is, back when the interstates were being built (the turnpike was mostly there first) the Turnpike Authority was in charge of the Turnpike, but Penn DOT was in charge of the Interstates. The issue arose when they couldn't agree on who would have authority/responsibility for the interchanges between them. So they agreed that they woudn't directly intersect.

There is a direct interchange with I-83 south of Harrisburg, but that's because 83 didn't become an interstate until the 60s or 70s.

A direct intersection of the Turnpike and I-95 is being planned, and should be completed in about 5 years. See http://www.paturnpike.com/i95/Default.htm .

The website also claims that this will solve the "Disjointed I-95" issue.

JS

Speaking of weird intersections, unless it's been rebuilt behind my back recently, in order to switch between S.H. 360 and I-30 in Arlington, TX, which are two major highways between Dallas and Ft. Worth, you have to go through the traffic light at Six Flags Road. When thousands of people are headed for Six Flags Over Texas on Saturdays in May or just about any day in the summer, that 90 degree turn can take a very long time.

This was originally done because I-30 used to be a turnpike (Dallas-Ft. Worth turnpike was the name I believe), and the exit ramp of a half mile or so was built for the tollbooth.

There are a few other intersections on I-30 between Dallas and Ft. Worth where you drive and drive and drive in a big circle, eventually arriving at the intersecting road. This is no big deal in Grand Prarie since there's nobody there (no offense, just an observation), but over by that stupid baseball stadium, it was a mess until a normal intersection was built a few years ago.

Also, there seem to be fewer exits off I-30 than what you would normally find on an urban Interstate. I presume this was also done to cut down on the cost of constructing and running the tollbooths.

So, this brings about a question from me: Why does the Dallas North Tollroad seem to have exits at a normal frequency with small tollbooths at each one? There aren't any half-mile exits over there, and there's plenty of traffic.

swag

You're right about I-30. To go from Southbound Loop 12 to Westbound 30 should be a simple 90 degree right turn. Instead, it's a combination of rights, lefts, and u-turns that add up to 630 degrees of turning. There was an article in the Morning News about a month ago on this - they want to rebuild the intersection, but the $ is years away, and meanwhile there are some folks campaigning to put the tolls back.

As to the Tollway, you'll notice it's designed that the majority of ramps are untolled.

[For the uninitiated, there are 3 main toll plazas that collect tolls from all vehicles. Between these, smaller tolls are collected on on/off ramps, but only in one direction. For example, at Mockingbird Lane, cars entering northbound pay the toll; cars heading southbound do not, since they will encounter the main barrier very shortly].

Look at a map here:
http://www.ntta.org/pub/pub/pub_rd_i...idth=2&level=2

Between NW Hwy and 635, there are 4 (untolled) exits to/from the south at walnut, royal, forest, and harvest hill. But there's only 1 (tolled) ramp to/from the north, at royal.

I don't know if this design was a result of learning from I-30, or maybe the design was possible because of the imbalance of traffic flow, assuming that a majority of the traffic was going all the way to/from downtown. So fewer ramps were needed to support for example, a trip from Lovers up to Arapaho.

Canarsie

For anyone who is interested:

Ten Most Dangerous Foods to Eat on the Road.

CrazyOne

I dunno about the rest of the story, but I do know in all those cases except where the interstate used an existing road the Turnpike was around first. It's 50-60 years old in the midsection. They're also building a direct connection with I-79 at Cranberry (old interchange 3). I dunno about the I-95, but this one is actually under construction and will be done in spring 2004. And because of the new process on the western end of the Turnpike, the I-79 "Cranberry Connector" will be a really direct connection, no tolls/tickets or anything.

See http://www.cranberryconnector.com/

Canarsie

I know what JS and swag are talking about, as I have been to Dallas a number of times. Allow me to relate my own personal story, as I believe this thread should serve to be just as helpful to other FlyerTalkers who drive as it is interesting...

After landing late at night at Dallas-Fort Worth International Airport, I drove on Interstate 635 east to the Dallas North Tollway south. I was tired and looking forward to relaxing and retiring in my hotel room for the evening.

When I approached the Northwest Highway exit, there was a double toll booth: one with an automatic machine for exact change, and one which was supposed to be manned by a toll collector.

Imagine my surprise when the only booth that was opened was the exact change booth, and I did not have exact change! After sitting in my car for about 30 seconds wondering what to do as a few cars behind me were honking their horns, I simply drove on and did not pay my toll. I never took the Dallas North Tollway again, as I do not like breaking the law.

Even though I have taken the Garden State Parkway (or GSP, as in the airport code you use in Greenville-Spartanburg, JS, or as in the Georgia State Patrol) in New Jersey numerous times, I once encountered the same exact problem as on the Dallas North Tollway, only this was years earlier as I exited from Interstate 78 westbound to the Garden State Parkway southbound late at night. The toll was 35˘, and this was before E-ZPass was available. I felt I had no choice but to skip out on paying that toll too.

I usually have the correct change on me, but was I wrong in skipping the toll? How can a toll road not have someone to give change if one does not have the exact change for the automated toll machine? What does one do in a situation like I have just described? Has this happened to anyone else?

[This message has been edited by Canarsie (edited 07-11-2003).]