How Is Data Specifically Defined in Algebraic Topology?

[dkotschessaa]

Sometimes while poking around for stuff in topology or algebra I find the word "data" used in this context, i.e. in Hatcher: (https://www.math.cornell.edu/~hatcher/AT/AT.pdf)

the data needed to do this is a map $f : A \rightarrow X_0$, for then we can form a quotient space of $X_0 \cup X_1$ by identifying...

Does it just mean "information" in a general sense or is there some precise algebraic meaning?

It's impossible to just look up, since the word has so many other meanings.

-Dave K

 

[jedishrfu]

Here's more data for your data but not sure if it's enough data to answer your data question.

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

Oh where is Commander Data when you need him?

 

[dkotschessaa]

Here's more data for your data but not sure if it's enough data to answer your data question.

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

Oh where is Commander Data when you need him?

This is what I meant about it being impossible to look up. If you search for "topology" and "data" you get stuff like that (which I have some familiarity with, but thank you). So unfortunately, this data about data is not the data about data that I was looking for, but data about data that I already had some data about.

I've seen the term pop up in algebra too. But nobody defines it. It just seems to means "here's some information" in which case, why say "data."

-Dave K

 

[jedishrfu]

In the words paraphrased from Seinfeld (the soup episode):

No DATA for you!

 

[dkotschessaa]

 

[FactChecker]

I would worry more about the formal meaning of "information" than a formal meaning of "data". There is so much information theory that you wouldn't want to get tangled up with. "Data" is probably a better general term with fewer presumptions.

 

[dkotschessaa]

I would worry more about the formal meaning of "information" than a formal meaning of "data". There is so much information theory that you wouldn't want to get tangled up with. "Data" is probably a better general term with fewer presumptions.

Sure, but I still don't have a definition in this context. It just sort of shows up like a family member who I am supposed to know about but somehow don't!

It's not super important, of course. But I am just wondering why it's being used.

-Dave K

 

[FactChecker]

Sure, but I still don't have a definition in this context. It just sort of shows up like a family member who I am supposed to know about but somehow don't!

You can think of it as an informal "information" as long as you don't read information theory into it.

I am just wondering why it's being used.

Because it is better than "informal information without reading information theory into it". Is there a better alternative?

 

[dkotschessaa]

Is there a better alternative?

"The following map is needed..."