[FoRK] Machine-Learning Maestro Michael Jordan on the Delusions of Big Data and Other Huge Engineering Efforts

Dave Long dave.long at bluewin.ch
Sun Nov 16 02:18:48 PST 2014

> Is there a general alternative to the integer primitive? While  
> virtually never considered, the answer turns out to be yes:  
> intervals of countably infinite length. It changes the way your  
> data structures and algorithms are built — things like simple order  
> relationships go away, integer operations mean something different  
> — but it is also efficiently representable on computers designed  
> for integers. (Obviously they have a finite description sufficient  
> to precisely compute operations over them even if the literal value  
> is not enumerable.)

That change sounds like the motivation for my noodling on an  
informatics equivalent to Stokes' Theorem: how do we mechanically  
swap between functions on points evaluated over intervals and  
functions on intervals evaluated at points?

I currently believe that intervals are not that different from  
integers (consider the connection between lattice elements and  
lattice ideals), but that the representation change in passing  
between the two, at least as currently —our languages do not have  
many ways to say that a computation is what physicists would call  
"geometric"— expressed, results in many individually trivial but  
collectively fiddly changes in tables and flowcharts.  err, data  
structures and algorithms.

Then again, I have yet to get this boundary operator swap working  
cleanly to my satisfaction, so you could well be correct that the  
difference is more fundamental.


(BTW, I'd be curious what spatial algorithms you have in mind; in my  
limited experience, space having a very nice convexity means that  
plane sweep has sufficed; there are difficult routing problems, but I  
would claim the difficulty with these is due to the knapsack-like  
elements and not to the spatial elements)

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