Mathematics and the WWW

Section 2:
W3: Myths and Realities

14 April 1997

When the words appeared, everyone said they were a miracle.
But nobody pointed out that the web itself is a miracle.
                                                  E.B.White, Charlotte's Web

Can I avoid the World Wide Web?

Not if this trend continues:

Is this really exponential?

Check out the log plot. Irresponsible Web statistics say that users are doubling every 53 days; slightly less irresponsible statistics have it that Web users are doubling every year.

So can you avoid the World Wide Web?
Probably not in your academic life, even if you're at an Internet-challenged institution -- there's government pressure to get schools online and colleges are the recipients of all sorts of strange support (e.g. last year our admissions office discovered the Web and fired our president up to lead the charge to get us a Web page).

There will be isolated holdouts (emphasis on isolated) just as there recently were faculty in my college (not in mathematics!) who had their email printed out by a secretary. However, new Ph.D.s now come prepackaged with experience in using the Web, if not in creating Web pages.

If you have kids at home it will be hard to avoid it there, too.

But the questions more of us care about are whether the Web will do us any good, what we can expect in the future, and what our investment should be now.

But isn't it grinding to a halt? becoming the "World Wide Wait"?
Robert Metcalfe is the inventor of the Ethernet (see Glossary, next to last section). He is also the person who made packet switching speedy enough to be interesting: when he was a graduate student at Harvard he used queueing theory to increase the potential capacity of the Ethernet from 17 to 90 percent. Here's a diagram Metcalfe made in 1976:

Metcalfe warns that "back when Internet backbones carried 15 terabytes of traffic per month, the world's Ethernet capacity was 15 exabytes per month, a million times higher." (Exabytes, if you wonder, add up. While a terabyte is a 1 with 12 zeros after it, an exabyte commands 18 zeros.) But those were last year's numbers. Carrier of some 40% of backbone traffic, MCI now reports 250 terabytes per month. Just a small shift in local traffic onto the public Net can create catastrophic cascades of congestion. [George Gilder.]

So people paid attention when Metcalfe predicted that the Web would become gridlocked by 1996 -- especially since predictions of the Internet's imminent demise have been around since its inception and everyone has found some servers at some times to be maddeningly slow. Well, it's 1997 and
Metcalfe's prediction hasn't come true yet (knock on silicon). In fact, measurements by John Quarterman showed significant improvements from January 1994 to January 1995. You can examine daily animated geographical maps of delays in the Internet. I haven't been able to track down who said "the Internet works in practice but not in theory," but it may have been Metcalfe himself.

Bill Gates is apparently predicting that we'll have "essentially infinite [sic]" bandwidth within the decade. However, I imagine it will occasionally appear to be terribly slow when we first begin to download feature films, for example. I've also heard from someone who thinks there will be more that Gates is predicting only middle-sized bandwidth availability.

Isn't it impossible to find the wheat for the chaff?
Great strides are being made in the intelligence of search engines and how to use them, but it's still necessary to exercise human intelligence in making value judgments. Examillions of people are making annotated Web sites of their favorite URLs. A few interesting examples:

Many groups make "awards" for especially deserving sites, but things are happening so rapidly -- new sites appearing, "old" sites disappearing -- that it's impossible to list everything good in a given area.

As an example of pretty good software for finding mathematics (and some other things as well), think of a topic in undergraduate (or school) mathematics and try the Math Forum search engine. Do tell us if you know some good sites that we don't have! Also try out our "Power Search" option, which attempts to help organize users to make effective searches. Let us know what you think.

Wheat is sprouting all over the Web, and many careful cultivators are doing their best to help locate it. This is likely to remain an area of concern for some time, and we'd appreciate your suggestions and your volunteering to help.

What's good, bad, both good and bad about the Web?

What's good about the Web?
The Web offers an amazing opportunity for individuals to create materials within their special interests and expertise, and to share their creations widely. For example, mathematicians can easily share an interesting approach, an insightful image, a pretty proof, things that might not be worth the time and effort to publish or which they didn't do themselves, but which others might enjoy. For example, I'm very fond of the home page of Doron Zeilberger of Temple University -- but I've never met him.

It's delightful to encounter the fresh, the attractive, the provocative --

The Web can even humanize mathematicians and mathematics -- e.g. just check out the home page of EPADEL giant Herb Wilf (who in fact needs very little humanizing). If you'd like the dirt on the EPADEL section officers, here's what I could find.

What's bad about the Web?
It is often hard to find the wheat among the chaff -- there's a lot of poorly thought out, sloppy work and bad design out there, along with glitzy commercialism. (There's also a lot of thoughtful advice on how to make good pages.)

At the moment my favorite is against pages sporting objects that whirl, blink, wiggle around, send out messages, etc., etc. I will be first in line when somebody figures out a way to freeze pages so they move only when you let them. (Davide Cervone has some advice for avoiding vertigo.)

The Web can be hard to read, slow to download, offensive to the sensibilities and the morals. But hey, life's like that, too.

Grumbles about the Web
Here are some curmudgeonly shots at the Web:

What's good and bad about the Web?
It changes so rapidly that there's a sense of impermanence -- coupled with the real excitement of creation and discovery.

There's room for individual expression along with a lack of civilizing social forces.

No one really runs the Internet (except for a minute amount of decentralized control -- it's done by "decentralized interoperation." In its ruling on the initial challenge to the Communications Decency Act, the U.S. District Court for the Eastern District of Pennsylvania included this explanation of the decentralized nature of the Internet:

No single entity -- academic, corporate, governmental, or non profit -- administers the Internet. It exists and functions as a result of the fact that hundreds of thousands of separate operators of computers and computer networks independently decided to use common data transfer protocols to exchange communications and information with other computers (which in turn exchange communications and information with still other computers). There is no centralized storage location, control point, or communications channel for the Internet...

For a thoughtful, if ancient ('94), article about the origins of the World Wide Web and its attendant problems, one that points out both the good and the bad, see Relihan.

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Gene Klotz