Wolfram Research is planning to introduce a web tool/service that is apparently supposed to be "google with math" - searching for information and calculating answers to quantitative questions such as "How much did it rain in Boston last year?". I'm a bit skeptical that it'll be able to do much more than point to numerical sources. E.g. how would it handle a query like "Based on US federal government budgets, how much was spent on wages in 2005?" Could it really pull together all the sources needed to asnwer such a question?

Even if Wolfram Alpha works, I'm not enthusiastic about the creation of a "mathematical oracle" that people just have to trust knows what it's doing. Oh, I'm sure it'll provide references to where it got its data, and perhaps even allow you to peek at the equations it applied, if it does more than extract data it finds.

It'd be much more useful to define "web-math" - i.e. the HTML equivalent for math - letting people easily create and publish data and equations in the open for others to copy/paste/evaluate/correct/extend/apply.

NOT just a spreadsheet - it should make all equations and relationships and data sets fully visible. (The greatest flaw in the spreadsheet paradigm, IMO - hiding the assumptions inherent in the calculation structure - it made spreadsheets much more of a read-mostly "trust me instead of taking the time to understand" medium.)

The basic web-math engine would support easy creation of meta-equations - equations operating on and transforming equations, building on built-in arithmetic, logical and symbolic primitive operations, as well as previous meta equations. So someone could define a set of algebraic transformations, then build on that for symbolic derivatives, and others could improve or correct those.

But the base web-math engine wouldn't even try to enforce "legal" transformations. Instead, it would provide a means of linking/authenticating/differencing copied equation/data sets so people can quickly check that a system of copied equations or data is exactly the same as that originally published by a particular source - or see the specific changes someone has overlaid. If someone thinks they've spotted a bug in the algebraic transformation meta-set, they could publish a fix as an overlay on the authenticated rule set, along with examples to demonstrate the bug and their proposed solution.

Likely a non-profit "webmath foundation" would quickly arise that would maintain the set of common meta-equations everyone comes to trust, but let that sort of thing be an emergent property, rather than built into the base concept.

With web-math, implemented as a web browser extension I suppose, you wouldn't go to a trusted oracle to get your answers - you'd search for someone who claims to have solved similar problems, grab and if necessary modify or combine their work, play with it, and if you come up with something interesting (maybe a new type of rocket engine, described as an overlay to a published "rocket science math" equation set), then publish it for others to criticize or admire.

Avoid falling into the copyrighted content trap - publishing with web-math should inherently make the math content public domain. If someone doesn't want their data or equations copied, they can keep them hidden and ask people to trust them - they have no need for web-math, and people can decide whether to trust them.

If copying and claiming credit for others' work becomes a problem, something like the web-math foundation mentioned above could solve that by allowing people to record first publication of new equation sets. But I doubt it'll be a big issue except among professional mathematicians.


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