The Math Inside the US Highway System | Hacker News Reader

The Math Inside the US Highway System

betterexplained.com

123 pointsskolos79 comments

"However, the numbers follow a grid, with rules nobody told me."

I learned it from reading a state map about forty years ago. The legend succinctly explained the system. Without digging through a pile of paper maps, that might still be the case. Regardless, these rules are probably clearly documented from a simple web search, despite that no one has felt the need to "tell" the author what the rules are.

EDIT: "interstate numbering system" on DDG brings up the Wikipedia page as the first link, and that link explains it. There's no mystery here, though my query string does assume that one assumes a "system" to be explained.

And while I'm editing, state routes and U. S. Routes kind of follow the same pattern, especially the N/S and E/W designations. Would have to go search to verify other commonalities.

US routes are mirrored -- US 1/2 in the Northeast and US101/(Defunct)80 in California, with US 90 ending in Texas. The 3 digit routes -- except 101, because the Federal Highway System had a lot more exceptions -- tended to be more tenuously associated with their "parent" route.

US 101 isn't the only exception to the US route numbering ssystem. US 400 isn't a branch of any other US highway (not to mention there's no US 0), US 412 is not a branch of US 12, and US 425 is not a branch of US 25.

I have some sympathy for people who were never told this or who are too young to have had a reason to encounter it. I work in a university and the number of times I've been asked, "What floor is room 302 on?" by new students is greater than zero.

I think I've been in buildings where two-digit rooms were on the ground floor, and so 302 would have been on the "fourth".

Although one would expect university students not to need help with this...

That's the standard way to number floors in much of the world outside North America and East Asia.

The ground floor is zero, the first floor is up a single flight of stairs.

My university made the system a little more obvious, with numbers like 0.01, 1.10, 3.14, B.04, 2B.01.

I live in an apartment where the numbering system varies depending on the building, one of them has 11-- for the first floor, 12-- for the second, 13-- for the 3rd, and I think 10-- is "Terrace" level.

> Although one would expect university students not to need help with this...

Rather curious why you felt the need to make a comment of this nature.

To satisfy your curiosity, I meant only that one would assume admission to university would require a modicum of intelligence or perhaps even awareness, which intelligence and awareness would amply suffice for the task of reading basic hallway signs.

I always found the it interesting that when somebody tries to find something to feel better than someone else about, and they pick the most basic, mundane thing. Tying shoes, adding small numbers, reading hallway signs.

The scales have fallen from my eyes!

I think university was the first time I'd been anywhere with numbered rooms that were arranged in a structured fashion, though even that wasn't entirely consistent and many buildings seemed to have mostly named rooms.

After the way my secondary school was laid out, I'm not sure I can ever trust room 302 to be anywhere in particular, nor even to be the only one going by that number...

This could be a UK thing, though. See also? - https://news.ycombinator.com/item?id=12535580

Something along these lines explaining the US interstate numbering system goes viral roughly every year or so; occasionally a bit more often.

Just remember: https://xkcd.com/1053/

That precise cartoon was at the forefront of my mind when I wrote my comment (and tempered my comment somewhat). But for some things, you're not one of the 10K, you just haven't been paying attention.

The basics of the system (even numbers go east-west, odd numbers go north-south, etc) were explained to me by my mother when I was young, in what ended up being a failed attempt to instill a sense of direction in me.

I can't navigate for shit, but the lesson about the logic behind the highway system stuck with me. Years later, when I moved from Seattle to Rochester, NY for college, people who marveled at how far from home I had moved occasionally asked me how I would get to my parents if there was an emergency and I couldn't fly. It always surprised them when I explained, "Well, I'd get on I-90 going east. Three days later, I'll get off at exit 28 and I should be able to navigate from there."

... I explained, "Well, I'd get on I-90 going east. Three days later, I'll get off at exit 28 and I should be able to navigate from there."

You're going to be a long time getting to North Bend, WA if you start in NY and head east. Or perhaps your self-described sense of direction is so bad that you actually end up heading the right direction. :-)

Looking at the map, exit 25 is actually probably the one I want, too.

You are correct, though! Like I said, it was a failed attempt. If I hadn't started driving around the time GPS technology became commercially available, I probably would have become an accidental vagabond before I graduated high school.

I was aware of most of this, but it segues nicely with my latest interest in Adam Adamatzky's research using the slime mold, Physarum polycephalum, in a form of bio-computing [1].

The demos where oatmeal flakes are placed on a highway map of major cities in various countries, and the Physarum optimize the paths in ways that closely resemble some of the existing major roads is compelling. I am holding out on how correlated it actually is given highways have developed not only from old horse paths and such, but from civic planning.

My daughter is a Chemistry/Bio major, and I have told her about this, and asked her advice on how I might go about doing this at home. It seems easy enough under controlled circumstances, and it it just seems fun checking in hours later for a 'result'! So much so, I ordered his book "Physarum Machines: Computers from Slime Mould".

[1] http://uncomp.uwe.ac.uk/adamatzky/research.html

I did some work on Physarum. It is indeed fairly easy to do simple experiments with the slime mold. You just need some petri dishes and a dark, moist environment. Just don't expect nice results every time, sometimes the slime mold just growths in a completely unexpected way.

There's another rule this one doesn't touch. Route numbers that are divisible by 5 are considered major routes, and with a few exceptions go from one geographical extreme to the other -- Interstate 5 goes from Canada to Mexico, Interstate 80 goes from San Francisco to New York.

> Route numbers that are divisible by 5 are considered major routes, and with a few exceptions go from one geographical extreme to the other

They tend to be major, but only 11 of 19 (11 of 17 that exist) go from one geo extreme to the other. Sorry highway numbers are a hobby of mine (yes I know strange hobby).

5 ^: Mexico to Canada

10 ^: Pacific to Atlantic

15 ^: Mexico to Canada

20: Mid-Texas to Mid-South Carolina

25: Southern Texas to Wyoming

30: Texas to Arkansas

35 ^: Mexico to almost Canada

40 ^: Eastern California, to Eastern North Carolina

45: Entirely in Texas

50: N/A

55 ^: Gulf of Mexico to Great Lakes

60: N/A

65 ^: Gulf of Mexico to Great Lakes

70: Utah to Maryland

75 ^: Southern Florida to northern Michigan

80 ^: San Francisco to New York

85: Mid-Alabama to Mid-Virginia

90 ^: Seattle to Boston (longest in the country)

95 ^: Maine to Florida

Why are 50 and 60 excluded? Wikipedia seems to think they exist, but it could be wrong.

They were skipped for unknown reasons. US Highway 50 and 60 exist though. Could possibly be why. An Interstate 50 and a US 50 in close proximity would be...confusing.

Us highways 50 and 60 exist and the location of Interstate 50 and 60 would be kinda close to where US-50 and 60 are, so they were probably skipped to avoid confusion.

When the Interstate Highway System was first created, AASHTO had a rule that no Interstate and US Route with the same numbers could coexist in a state. Since with both numbering schemes, 50 and 60 would fall in roughly the same part of the country, I-50 and I-60 had to be skipped so they wouldn't share any states with Route 50 and Route 60.

AASHTO has since relaxed that rule, and there are now a few exceptions to it, but it's too late to shoehorn in two major interstates.

AFAIK, the old US Highways were numbered opposite to the Interstate system, at least for round-numbered routes. US-10, 20, 30, etc., more or less proceeded north to south, Interstates are increasing south to north. The middle numbers like 50 would possibly overlap in both systems so designations like I-50 weren't used.

Indeed they are. Route 1 mostly runs along the east cost (key word is "mostly") often next to I-95, and Route 99 used to exist right next to where I-5 is now (it's since been turned into a gaggle of state highways in CA, OR, and WA), while Route 2 runs in the north and Route 90 largely runs next to (or is co-signed with) I-10.

Yup, in fact there are 99W and 99E more or less straddling I-5 and running in generally north-south alignment in the Portland metro area. In recent years I-5 has become increasingly congested, not just in "rush hour". Consequently 99E/W are also heavily used as commuters try to escape traffic. Hard to solve the problems created by our success.

You ever get a twitch in your eye when you see I-238?

Every time.

99 is a real tearjerker too

I-69 and its three branches (69W, 69C, 69E) in Texas always gets an emotional response from me.

At some point decades from now, it won't be quite as bad because all the different segments of I-69 will be united. We'll still have a weird three-way split in South Texas, but north of the split they'll form a single highway going all the way to the Canadian border instead of the current disjointed highway segments. And there are parts of the country where I-69 fits in between I-65 and I-75, so while the name is awkward in Texas, that's not the case in the Indiana and Michigan.

But this will take decades due to limited funding and a bunch of states that just don't care. I'll be lucky to see it in my lifetime, and if I do, I'll be an old lady.

What weirds me out in that area, by the way, is that I-2 even exists. I grew up understanding that I-4 was the lowest-numbered Interstate in the country (and my family went to Florida often enough when I was a kid that I was quite familiar with that road), and it still hasn't quite sunk in yet that it got dethroned.

I-99 is particularly aggravating because of how it came into existence. At least I-238 exists by necessity. I-99 has its number because a showboating Congressman snuck the number in as a rider on a bill because he thought "highest possible two-digit interstate" would get his state some more tourism.

As such, I-99 is the only interstate AASHTO is forbidden by law from renaming.

I-40 is an interesting case. It hits the ocean in Wilmington NC, but doesn't make it to the coast in California, ending in Barstow. The completionist in me says that it ought to continue through Palmdale to Ventura.

Until a few years ago, it wasn't contiguous. There was a gap in Memphis where the locals objected to its completion because the traffic noise would have disturbed the animals at the zoo. So the northern part of I-240 was signed to include I-40, finally linking the two halves together.

Caltrans has a long-term plan to get I-40 extended to Bakersfield. It's probably not going to ever quite hit the ocean because the Coast Range west of there is pretty rugged, and the traffic continuing through is pretty minimal.

I agree with you on that one. I debated whether to count it as going from one extreme to the other since it stops about 150 miles short of the ocean, but I figured since it gets you most of the way, might as well count it.

> There was a gap in Memphis where the locals objected to its completion because the traffic noise would have disturbed the animals at the zoo.

A bigger reason is that the road would have run straight through Overton Park and required that the entire park be destroyed. People like Overton Park, and the protests over that got the project cancelled. In fact, they actually built the road east of Overton Park, but they stopped there when the protests started. What was intended to be I-40 is now called Sam Cooper Blvd. If you look at Google Maps, you'll see that the gap between the end of I-40 on the west side and the beginning of Sam Cooper basically just consists of Overton Park and a few blocks in each direction.

I'll agree with @Mikestew that this is pretty familiar territory. But it did get me looking to see how well the original Interstate planners did, in terms of leaving unallocated numbers available for future expansion.

Surprise, surprise: regional economies expand at different rates, which forecasters don't always get right. It's not as messy as Social Security numbers or area codes, but there are definite pockets of congestion.

For example, the East-West corridors between I-80 and I-90 have been graced with more highways than expected. We've had to come up with two versions apiece of I-84, I-86 and I-88 in different parts of the country, along with one I-82. By contrast, there's been no East-West build-out whatsoever between I-30 and I-40.

More details are here: https://en.wikipedia.org/wiki/List_of_Interstate_Highways

As to how we're planning to use up the numbers for future expansion, there's this Wikipedia page: https://en.wikipedia.org/wiki/Future_Interstate_Highways

Of course if you want to take the I-7 to Fresno, the future is now because it's called 99 but not yet built to interstate standards.

Which is funny because once that's done, that road will have been a US Route, a State Route, and an Interstate in that order.

SR 99 was originally part of US Route 99, but when I-5 was built AASHTO decided to decommission Route 99 since the whole thing paralleled I-5 so closely that it was considered redundant. The states, however, decided to continue to maintain (most of) the road, and it was assigned a number of state highway designations, including SR 99 in the Central Valley (the states, particularly Washington, did give up on a few portions of it, which are now maintained as local roads in various cities).

And now they want to make it an Interstate.

(Also, speaking of future Interstates, I'm kinda shocked that I-66 was cancelled. They upgraded a bunch of roads to Interstate standards, and they even signed the Cumberland Pkwy. in Kentucky as "Future I-66 Corridor" (you can even see it on Google Street View), only to give up on it.)

It's always interesting to see what gets posted and upvoted. Growing up before people generally had access to the internet, (when you had to use a physical map to find places), I'd heard these particular tidbits repeated ad nauseum every time our family took a road trip.

I wonder:

a) is this new to anybody?

b) if so, what other tidbits of "everybody knows that" are fading into obscurity because of technology? (Surely you all remember how to reshoe a horse in a pinch at least?)

a) yes, it is new to me because I was not raised in your country, not because the web came after I was born.

High school student here; completely new to me! To be honest I'd never thought about the highway number system before

It's (somewhat) new to me but I'm an immigrant.

The fun part is when you're traveling westbound on I-580 in Berkeley, CA... and you're simultaneously going eastbound on I-80... on the same stretch of road.

Or the place near Trenton, NJ where I-295 North becomes I-95 South, and vice versa.

The UK's roads have a numbering scheme: https://en.wikipedia.org/wiki/Great_Britain_road_numbering_s...

They encoded real information into their primary key. They're going to run into trouble when they need to change one of these roads later.

(Like maybe rotate one of these North-South roads to run East-West.)

Road direction can be ambiguous. Fairly obvious with a loop like I-270 around Columbus, Ohio. I've thought they should have designated the direction as clockwise and counterclockwise, going around the loop for a significant portion gets confusing re: "North" which may be actually east or west.

Also I-84 in western Idaho is more north-south even though it's even-numbered and nominally and east-west highway. Probably not too confusing because roads are much more sparse in that part of the country, people navigate on the basis of destinations, the exact direction is kind of hypothetical.

No surprises in it though, real-world roads won't follow the abstract grid very closely, there are going to be quite a few exceptions.

In Charlotte (and other places, I'm certain) the signs referencing I-485, the local loop interstate highway, refer to "Outer" and "Inner", which is just as useful as long as you know to drive on the right!

Louisville, KY has a definite hub and spoke layout with both I-264 (East/West) and I-265 (North/South) as increasingly outward rings (and several state routes and major parkways are additional "rings" in between). Many natives don't know the cardinal directions of the interstates or state routes and there's a lot of landmark-based navigation (towards the Fairgrounds/Airport, away from Downtown, et al). I like using clockwise/counter-clockwise directions myself and after an initial bit of confusion it's fun when fellow natives blink a bit and recognize it's not a bad system. (Thus far haven't made any converts to it, though.)

Further aside, given the the similarity in numbers of I-264 and I-265 they are more commonly referred to by their expressway names, the Watterson and the (Gene) Snyder, respectively. Louisville is one of the few cities I know of where you'll meet natives that don't actually know the interstate numbers they drive on sometimes every day, you have to mention it by name to get the right directions.

Why do the Boston and Washington Beltways have the same number (495)?

https://en.wikipedia.org/wiki/Interstate_495_(Massachusetts)

https://en.wikipedia.org/wiki/Interstate_495_(Capital_Beltwa...

> Because longer interstates may have many such supplemental routes, the numbers may repeat in each state along their route, but they will not repeat within a state.

https://en.wikipedia.org/wiki/List_of_auxiliary_Interstate_H...

Spur and belt routes, the ones with three digits, are reused across states. They tend to be ones that branch off to serve particular cities and not cross state lines.

I assume because they are both loops that spur off of 495. It's definitely confusing, but it seems consistency in numbering won out over unique-ness.

You mean both loops spur off 95 :-) but yeah that makes sense

I-495 used to be the name of the Maine Turnpike, as well, before 2004. Now it that route is included in I-95, while the previous I-95 is now labeled I-295, while a yet third section of highway connecting the two above Portland is now technically 495.

But I-495 is not signed as such; it is simply called the 'Falmouth Spur' ;)

Because there are so many auxiliary routes that they have to get reused. The main rule is that they can't be in the same state, although that's not necessarily enough to guarantee that the names don't get confusion. I-395 is the spur of 95 in Virginia into DC and the spur of 95 into Baltimore, while 695 is both in DC and in the Baltimore suburbs, which are about an hour apart in driving terms.

Some states (e.g., Indiana) have grids similar to the Interstate and US routes. Others have different systems: in Florida the first digit tells you roughly where in the state it is, from 1xx routes in the Panhandle to 9xx routes around Miami. And still others just assigned numbers in order of construction, so on a map it makes no sense at all.

I wouldn't call it very math-y, I'd call it a systematic numbering scheme.

I-82 in Washington State is a glaring exception to the numbering convention, being located north of I-84. Are there other exceptions?

Another glaring exception is Interstate 238 in California. It's an important, if short, route in the Bay Area, but at the time it was redesignated an Interstate, every x80 number had been taken, either by other local freeways, or by unrelated highways. So, when it was updated to interstate standards, they just decided to let it keep its old number, even though interstate 38 doesn't even exist.

Since then, Highway 480 (it was never formally adopted as an Interstate) has been removed, but renumbering would be more trouble than it's worth, so it's remained I-238.

There's also I-595 between DC and Annapolis, which is signed as US-50 instead because there are too many x95s in the area.

There's a simpler explanation. It's a pre-existing route that was adopted by the federal highway system. US 50 is well known enough that resigning it would be more trouble than it was worth.

Interstates don't usually spring out of thin air, they're often existing US Highways or state roads that get relabeled or upgraded to interstate standards and relabeled.

Many Interstates share numbering with US Routes. It's a way to keep around some US Routes that share some of their path with an Interstate but then diverge sharply in other areas without having to maintain two roads in parallel

Head over to Google Maps and zoom in on some random Interstates; you'll see the dual numbering. A good example is I-10 and Route 90 in southeast Texas. Everything between roughly Columbus and Vinton (including the whole Houston area), I-10 and Route 90 are the same road, but they go their separate ways on both sides. Or for a north-south example, I-35E and Route 77 in the Dallas area; they're joined between Denton and Waxahachie.

Same thing happened to US-74 in North Carolina. Parts of it are I-74 despite being south of I-40.

I-99 is in the middle of Pennsylvania.

There's a fun bit of trivia to that; it's actually I-84 that's the exception.

Back when the Interstate Highway System was created, it was designed with intentional forks in the road that will both go to the same start and end points but get there in different ways. These forks shared the same number but had directional indicator suffixes. One example of this was I-80S and I-80N.

Eventually, AASHTO decided that system was confusing, so they decided to eliminate most directional suffixes and assign unique numbers to each highway. As such, I-80S became I-80, and I-80N became I-84. They would've used I-82, but that highway already existed, and they decided against resigning an existing non-suffixed interstate.

Some directional suffixes continue to exist, but only for interstates that fork for the duration of a single metropolitan area with two principal cities. The best-known example of this is I-35, which forks into I-35E and I-35W twice, once in Dallas-Fort Worth and again in Minneapolis-St. Paul.

Except where the numbering is magical such as the renaming of hwy666 when some groups suddenly decided the number was satanic[1]

[1] https://en.wikipedia.org/wiki/U.S._Route_491

Route 666 was renamed because people kept stealing the signs for novelty value, and it was costing the state too much money to keep replacing the signs again and again and again. IIRC, they even rolled out signs that were supposedly "theftproof"; they got stolen anyway, and it cost the state a lot of money to develop them.

Same with mile marker 420 in Colorado on the I-70.

And vandalism btw. Particularly the preparation needed to remove a 'theft proof' sign is not done by an idle souvenir collector on a road with essential no tourists that no one form outside the area has ever heard of. Those things are just as likely done by the few who have a moral objection to the number. Ironically, the road could have been turned into a minor tourist attraction for Gallup if not Shiprock. Likewise, copies of the sign could have been pedaled in Gallup to feed any souvenir collectors as is done with rte 66 signs.

But most interesting to me is the way the attitudes of evangelicals concerning the spiritual status of the valley (albeit newly acquired and negative) spilled over into the Navajo beliefs as the area become known on the reservation to have a high number of Skinwalkers.

Metro Boston is a fantastic region with which to illustrate the flawless order of the highway system's numbering!

more an encoding than "math"

The US interstate numbering system is fairly common knowledge. Does it by itself really deserve a post here?

Perhaps this is interesting to folks outside of the US. It's common knowledge to US people only.

I've lived in america my whole life and the way only things I knew were (1) even was west/east and odd was north south and (2) ABB highways branch off of BB (405/5 for example)

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