Mathematical Search and Regular Expressions

[Owen Densmore]

Some of us have been discussing the relationship between mathematics  
and computation.  One particular element of this is how math is a  
second class citizen within the web and computing world.

Its tough for me to send you an equation, for example, one with a  
standard representation and easily input into your particular math  
software (MatLab, Maple, Mathematica).  The specialization of math  
software bears this out .. all the packages are quite expensive and  
not particularly interoperable.  MathML has not matured and is not  
yet ubiquitous, nor can it be used as input to these math packages.  
TeX can typeset math, but has no semantics tied to it.

One particular example came to me yesterday while thinking about  
searching for certain kinds of exponentials: How would I search for  
an equation on the web, and how could I "grep" through a set of  
papers using a regular expression containing mathematics?

The semantics of mathematical notation has to be considered in regex  
as well: a*b is the same as b*a, and the regex engine would have to  
know that.

I'm wondering if this is just that math has not yet had its day in  
the web sunlight, or it is deeper .. a fundamental problem.

     -- Owen

Owen Densmore   http://backspaces.net

[Marcus G. Daniels-3]

Owen Densmore wrote:
> How would I search for  
> an equation on the web, and how could I "grep" through a set of  
> papers using a regular expression containing mathematics?
>
> The semantics of mathematical notation has to be considered in regex  
> as well: a*b is the same as b*a, and the regex engine would have to  
> know that.
>
>  
XPath/XQuery would work pretty well for regex-like queries of
hierarchical MathML (XML) expressions.   The bigger problem is getting
people to publish it.   As a starting point, arXiv archives and parses
LaTeX, which it renders to PDF.   A system like arXiv that is set up to
process user input for a search engine could be elaborated to do, for
example, LaTeX -> MathML conversions (just for the sake of making search
systematic) and over time to encourage authors to provide MathML input
that was machine readable by Mathematica, etc.

[Giles Bowkett]

> > How would I search for
> > an equation on the web, and how could I "grep" through a set of
> > papers using a regular expression containing mathematics?
> >
> > The semantics of mathematical notation has to be considered in regex
> > as well: a*b is the same as b*a, and the regex engine would have to
> > know that.
> >
> XPath/XQuery would work pretty well for regex-like queries of
> hierarchical MathML (XML) expressions.   The bigger problem is getting
> people to publish it.   As a starting point, arXiv archives and parses
> LaTeX, which it renders to PDF.   A system like arXiv that is set up to
> process user input for a search engine could be elaborated to do, for
> example, LaTeX -> MathML conversions (just for the sake of making search
> systematic) and over time to encourage authors to provide MathML input
> that was machine readable by Mathematica, etc.

The lack of a common format is the real problem. That's cultural
rather than technological. You see math on the web as gifs, PDFs,
MathML, all kinds of different things.

There's a company called Powerset which is working on Web searches via
natural language processing. That might result in some improvements
for math searches but it really doesn't solve the problem.

Google Code and koders.com both deal with problems that are kind of
similar, but not really.

--
Giles Bowkett
http://www.gilesgoatboy.org
http://gilesbowkett.blogspot.com
http://gilesgoatboy.blogspot.com

[Martin C. Martin-2]

I think Barbie summed it up best: "Math is hard."

Even most people who are good with computers find math hard.  There are
many programmers who have trouble thinking in recursive/dynamic
programming terms, or who have trouble with the sort of simple 3D vector
math found in games.  As such, searching for exponentials, or putting
them on the web, just doesn't come up that often.  If it did, it would
be a bigger part of HTML/wiki/whatever.

At least, that's how it looks to me.

Best,
Martin

Owen Densmore wrote:

> Some of us have been discussing the relationship between mathematics  
> and computation.  One particular element of this is how math is a  
> second class citizen within the web and computing world.
>
> Its tough for me to send you an equation, for example, one with a  
> standard representation and easily input into your particular math  
> software (MatLab, Maple, Mathematica).  The specialization of math  
> software bears this out .. all the packages are quite expensive and  
> not particularly interoperable.  MathML has not matured and is not  
> yet ubiquitous, nor can it be used as input to these math packages.  
> TeX can typeset math, but has no semantics tied to it.
>
> One particular example came to me yesterday while thinking about  
> searching for certain kinds of exponentials: How would I search for  
> an equation on the web, and how could I "grep" through a set of  
> papers using a regular expression containing mathematics?
>
> The semantics of mathematical notation has to be considered in regex  
> as well: a*b is the same as b*a, and the regex engine would have to  
> know that.
>
> I'm wondering if this is just that math has not yet had its day in  
> the web sunlight, or it is deeper .. a fundamental problem.
>
>      -- Owen
>
> Owen Densmore   http://backspaces.net
>
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

[Robert Howard-2-3]

Math ability and music ability are related. Similar to Owen's question, I
would love to know how to search for a song on the internet given that I
only know how to hum a few bars.

-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf
Of Martin C. Martin
Sent: Tuesday, December 26, 2006 4:14 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Mathematical Search and Regular Expressions

I think Barbie summed it up best: "Math is hard."

Even most people who are good with computers find math hard.  There are
many programmers who have trouble thinking in recursive/dynamic
programming terms, or who have trouble with the sort of simple 3D vector
math found in games.  As such, searching for exponentials, or putting
them on the web, just doesn't come up that often.  If it did, it would
be a bigger part of HTML/wiki/whatever.

At least, that's how it looks to me.

Best,
Martin

Owen Densmore wrote:

> Some of us have been discussing the relationship between mathematics  
> and computation.  One particular element of this is how math is a  
> second class citizen within the web and computing world.
>
> Its tough for me to send you an equation, for example, one with a  
> standard representation and easily input into your particular math  
> software (MatLab, Maple, Mathematica).  The specialization of math  
> software bears this out .. all the packages are quite expensive and  
> not particularly interoperable.  MathML has not matured and is not  
> yet ubiquitous, nor can it be used as input to these math packages.  
> TeX can typeset math, but has no semantics tied to it.
>
> One particular example came to me yesterday while thinking about  
> searching for certain kinds of exponentials: How would I search for  
> an equation on the web, and how could I "grep" through a set of  
> papers using a regular expression containing mathematics?
>
> The semantics of mathematical notation has to be considered in regex  
> as well: a*b is the same as b*a, and the regex engine would have to  
> know that.
>
> I'm wondering if this is just that math has not yet had its day in  
> the web sunlight, or it is deeper .. a fundamental problem.
>
>      -- Owen
>
> Owen Densmore   http://backspaces.net
>
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org

[James Steiner]

http://hsearch.nayio.com/

Nayio is a hun-driven music search engine. It is still in early beta,
and its database of songs is still tiny. I haven't given it even a
cursory look yet (I just saw the announcements about it a short while
ago, and remembered).

Seems like it would be a good candidate for community-provided
content... users (with good humming ability) hum known songs,
providing the hum-data that searching users hums are compared against.

~~James
http://www.turtlezero.com
(JA-86)

On 12/27/06, Rob Howard <rob at symmetricobjects.com> wrote:
> Math ability and music ability are related. Similar to Owen's question, I
> would love to know how to search for a song on the internet given that I
> only know how to hum a few bars.

[Justin Lyon-2]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Martin,

The intellectual desert is vast.

Thinking is hard. Most people dislike thinking. Thinking scientifically
and mathematically is even harder. Addressing complex problems is even
harder.

It's a sad fact.

That's why they hire people like us; to solve the difficult problems and
make them money.

There's a reason why they call us the cognitive elite.

:-P

- --
Best regards,

Justin Lyon

M: [phone] (Worldwide)

M: [phone] (Lisbon, Portugal)
M: [phone] (London, UK)

O: [phone] (San Antonio, USA)
O: [phone]  (London, UK)
E: justin at simudyne.com
W: http://www.simudyne.com

Martin C. Martin wrote:

> I think Barbie summed it up best: "Math is hard."
>
> Even most people who are good with computers find math hard.  There are
> many programmers who have trouble thinking in recursive/dynamic
> programming terms, or who have trouble with the sort of simple 3D vector
> math found in games.  As such, searching for exponentials, or putting
> them on the web, just doesn't come up that often.  If it did, it would
> be a bigger part of HTML/wiki/whatever.
>
> At least, that's how it looks to me.
>
> Best,
> Martin
>
> Owen Densmore wrote:
>> Some of us have been discussing the relationship between mathematics  
>> and computation.  One particular element of this is how math is a  
>> second class citizen within the web and computing world.
>>
>> Its tough for me to send you an equation, for example, one with a  
>> standard representation and easily input into your particular math  
>> software (MatLab, Maple, Mathematica).  The specialization of math  
>> software bears this out .. all the packages are quite expensive and  
>> not particularly interoperable.  MathML has not matured and is not  
>> yet ubiquitous, nor can it be used as input to these math packages.  
>> TeX can typeset math, but has no semantics tied to it.
>>
>> One particular example came to me yesterday while thinking about  
>> searching for certain kinds of exponentials: How would I search for  
>> an equation on the web, and how could I "grep" through a set of  
>> papers using a regular expression containing mathematics?
>>
>> The semantics of mathematical notation has to be considered in regex  
>> as well: a*b is the same as b*a, and the regex engine would have to  
>> know that.
>>
>> I'm wondering if this is just that math has not yet had its day in  
>> the web sunlight, or it is deeper .. a fundamental problem.
>>
>>      -- Owen
>>
>> Owen Densmore   http://backspaces.net
>>
>>
>>
>> ============================================================
>> FRIAM Applied Complexity Group listserv
>> Meets Fridays 9a-11:30 at cafe at St. John's College
>> lectures, archives, unsubscribe, maps at http://www.friam.org
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org

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