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Wednesday, July 18, 2012

Superadditivity

In Mathematics, if following inequation is true, for every x an y of a certain domain,


f(x+y) \geq f(x)+f(y)\,.

we speak about superadditivity.

Source: http://en.wikipedia.org/wiki/Superadditivity

How to translate this in Photography? Well, normally superadditivity is said when the combination of two developers is stronger than each of them alone. Yes,but it is still difficult to say when there is superadditivity of two developers. Sure, if you develop with X g/l of, say, Parodinal, you have more developing time than with 2X g/l. But one developer is not said to be superadditive with itself. It is just stronger. Suppose that  we want to stablish if Caffenol and Parodinal are superadditive. What experience must be done? If you have X g/l of Parodinal and Y g/l of coffee mixed (other parameters constant like pH and so on) in a solution, then we speak about a stronger equivalent concentration of just Parodinal. In this case, if the development takes less, is faster, no wonder. But if we have tow separate solutions, one of X g/l of Parodinal and other with Y g/l coffee, each of them has a developing speed. In this case the sum of the two is to develop in Parodinal and then in Caffenol.

We have, for example, a Parodinal solution that develops in half an hour and a Caffenol in 45 minutes. We develop 15 minutes in Parodinal (for instance) and 22,5 minutes in Caffenol, one after the other (neglecting the effect of mix). This means that theoretically we need 37,5 minutes for the development. Well, then let us make F(Xg/l+Yg/l) by mixing equal parts of the developers. One should expect the same time as above. Well if this time is then shorter, for any X and Y combinations then, and only then, we may have superadditivity, I think.


Recently I thought I found superadditivity between Caffenol and Parodinal but I am not sure now, I have to undertake new experiments. I only can say that if you add Parodinal to any Caffenol you have a faster 'Caffenol' because more Coffee doesn't bring more speed, Caffenol is allways slow. But when you add Caffenol to Parodinal, it is slower than putting more Parodinal to the existent, so the Caffenol slows Parodinal for an equivalent only parodinal concentration. Because Parodinal is faster when its concentration is rised.


On the other hand, what kind of developer do we reach adding these two? A better Caffenol but a worst Parodinal. More grain, unless you want it, finer than just Caffenol. I would say, not tried yet, that Coffee works better with Vitamine C, than with Parodinal.


Caffenol plus Parodinal

Parodinal 1:250



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