# Thread: Simple formula to calculate maximum error term for EI

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Mar 2008
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## Simple formula to calculate maximum error term for EI

Hi all,

I tried searching the forums but I haven't found anything similar so I thought I would post it. This is just a simple formula with an explanation on how the calculation works.

Lets say you do Waterchanges at regular intervals (could be weekly, every 3 days, etc) and let X be the percentage water change you perform expressed in decimals. Meaning a 50% water change gives X=0.5. 40% WC gives X=0.4 and so on. Now given your current EI dosing scheme calculate how much of an element you are adding in between successive water changes. Call this Y.

Lets say you add 4ppm NO3 every day, and do weekly 50% water changes. Then X=0.50 and Y=4x7=28 (4 ppm over 7 days equals 28ppm). To calculate what level your NO3 value will plateau off at (making the simplifying assumption of zero uptake by plants...ie a worst case scenario) this is how your NO3 levels will look.

Week 1: Y
Week 2: Y+(1-X)Y

Note: (1-X) is the fraction of elements remaining in the tank after doing the waterchange.

Week 3: Y+(1-X)Y+((1-X)^2)Y
...
Week N: Yx(1+(1-X)+(1-X)^2+(1-X)^3+...(1-X)^(N-1))

Now the sequence in X is a simple geometric progression. If you let N tend to infinity, ie you are looking at the long term plateaued level of NO3 in your system the sum can be simplified and you end up with the following expression:

Final Plateaued Level= Y/X

So for example as mentioned by Tom in various threads if you do 50% WCs, or X=0.5 then your Max error is Y/(0.5)=2Y
i.e. twice the amount you dose between water changes.

Similarly 60% waterchanges give X=0.6 and thus gives the max error of Y/0.6=1.667Y

I just thought it might be an easy reference for people to figure out the maximum error they can have while dosing using EI so that they can be reassured that even if Sh*t happens, they won't harm their fish.

Cheers

2. thanks, I'll add this to the EI article so folks can see that one does not merely have to accept 50% WC's and the typical 2X build, up or if they wish to do fewer water changes.

I'm not sure why so many adhere so rigidly to things when it comes to methods.

But they do tend to do that.

Regards,
Tom Barr

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You're very welcome Tom. I'd just like to add that I really really appreciate all the info on this forum and all your research into various aspects of planted tanks. I'm from a scientific background myself (Ph.D student) and I really appreciate your scientific approach towards all your experiments and the fact that you always make it a point to qualify all your suggestions/opinions with reasons.

After spending the whole of yesterday and today scouring through all the articles and other great threads on the forum I think I finally have the confidence to start my own planted tank and I don't feel clueless about following various peoples conflicting advice blindly.

Regarding the WC scheduling, I agree with you. I think this might help re-assure people about how changing their WC schedule will impact the maximum possible buildup. Then it is a matter of personal preference based on how comfortable someone is with the max buildup for his/her WC scheme.

Cheers

4. Well EI and most methods where never meant to be so rigid!

If so, it was the ego of the person selling it or fear someone might use another method that was not "theirs".

Such steer manure does not help the hobbyists nor help the hobby.

Some might want tighter control, daily dosing, larger more frequent water changes, or the opposite: less work etc.

Sometimes common sense flies out the window.
This is true with PhD's and folks with less formal education.
Sometimes common sense is even less prevalent with more educated types.
I know you have seen it if you have gone this far in school.
I will not lose that nor my humor, as much as they try to beat it out of you.

Regards,
Tom Barr

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Heh, yeah, much of what you say is true. Although I must say that in Physics/Engineering at least you don't have hundreds of thousands of people on forums talking about their own DIY "science" that worked for them in their backyard/basement . In your profession you do have to deal with a huge community of enthusiatic hobbyists which is a good thing in a way but a lack of peer review for various theories floating around, and everyone claiming that one thing is the end all and be all because "it worked for them" gives rise to a big mess with ill informed theories being firmly grounded and followed blindly. As you've mentioned before a lot of people incorrectly mistake correlation for causation which is quite unfortunate. Ofcourse they can't always be blamed because this is a common mistake made in most fields in academia. So I agree with your philosophy in always keeping a clear head and thinking things out with good common sense and testing and trying things out for yourself without blindly committing to an idea or belief.

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Orion,

What are you getting your PhD in? I'm a materials engineering student at UAB in Birmingham, AL. I'm trying to decide if I want to grad school or not, how do you like it?

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Hey Creighton,

I'm doing my Ph.D in Applied Engineering Physics at Cornell, NY. Personally I love grad school but I think it varies drastically between different people. A large part of it depends on your advisor and what his/her temperament is like and how he is with managing his students.

I have 2 friends who are both smart guys but didn't get along at all with their advisors (mostly the advisor's fault. Both of them were hot headed and nasty with their students) and have now left with a Masters. My advisor on the other hand is a great guy who lets me keep flexible timings as long as I get results, is good at encouraging me and keeping me motivated to do work without being nasty or too pushy (which can have a very demoralizing influence). So I think my biggest piece of advice would be to carefully select your advisor....talk to his/her grad students to find out what the lab dynamics are like and how much you are expected to work, etc. I enjoy my grad life because I like my research but I also get my weekends off to do my own thing and in general pursue my hobbies. Some advisors however can be slave drivers and don't let you do that as much, and I'd be completely miserable under them even if I loved my research.

Apart from that I think there are certain things you should be prepared for. If you do go in for a Ph.D, you're not going to be earning much for a good 4-6 years which is a fairly long time and you need to figure out if thats OK with you. Personally I don't care so much, I still make enough to live quite comfortably in a collegetown area and pursue hobbies like Aquariums, rock climbing, etc. I'm definitely not poor , but nor do I have huge savings or the ability to buy a fancy new car/house. I'm OK with that, but for some people it might be acceptable at 21-22 when they start but they get frustruated with it by the time they are 24-25.

Now the nice thing about it is that if you have a nice advisor, you can be like me...typing this at 11 AM from home...having woken up just 30 mins back . Flexible timings is the single most awesome thing for me in grad school. I love being able to do stuff on my own terms and timings and not have to follow the regular 9-5 type patterns.

8. Originally Posted by orion2001
So I agree with your philosophy in always keeping a clear head and thinking things out with good common sense and testing and trying things out for yourself without blindly committing to an idea or belief.
Which is why I try to impose the Socratic method.
They need not convince me or have faith in me, just themselves.
Through their own logic, their own test, their own eyes, will the truth they seek be shown. I just suggest the method and ask the questions to help them get there.

The simplified infinite series example was shown about 1996 on the Krib(see PMDD) but this is another twist on it. Just to get the max error for your routine.

But you have to give folks a break also. So with the general public, you need to help those you can, and the relatively few that you cannot, do not waste too much time on.

Even if they come across as a nut at first, keep with them, many are just totally frustrated and uncertainly is a principle Hiesenburg understood all too well.

Regards,
Tom Barr

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