# Why is a measured true value “TRUE”?

So, I am studying counts and errors currently...and, there is a concept of true value (the real value to which every other measured value is compared to).

So, I had a question that why is the True value true. I mean, the true value must have been measured by something / an instrument calibrated to something(and, I am not talking about SI units and what-not, because I don't think a company making weight equipment is gonna check the calibrator each time with the model kept at a SI center)... Anyway, the true value has been measured by a instrument and there may be a error in that too...so, as per me, this leads to a round of circular referencing among different calibrators and instruments...

So, why is a True value true...and, if it is just an average of measured values...well, that leads to even more doubts

P.S. I may be completely unaware of things and, this question may be nonsensical...so, sorry in advance and..

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Regards, Nerd951

• See true value May 13, 2021 at 15:12
• See also Measurement value and true value: "It is impossible to take a perfect measurement i.e. one that would give an exact true value for the property being measured. In practice the best we can do is to determine the upper and lower limits of a range of values within which the true value lies." May 13, 2021 at 15:13
• All physical measurements contain error no matter how much precision your instrument has, and every time the value we measured a same quantity is a random variable, usually we need to measure many times and average it to get the expected value as best guess of true value per law of large numbers (LLN) (en.wikipedia.org/wiki/Law_of_large_numbers) May 16, 2021 at 2:36
• Thanks a lot Mauro and @Double Knot.....much appreciated May 16, 2021 at 13:50
• The True Value is at the Hardware Store... You could read Longitude by Dava Sobel for more background. Sep 18, 2022 at 1:35

I'd say, it is a state in a logic table, connecting initial or known states, to variables or unknown outputs. Computing involves two-valued logic, and so true is often equated to signal, and false to no signal - these can often be gate voltages that control larger currents, it's important to have accurate enough voltage discrimination. In practice true is always contextual, it depends on your model, & circuits are just one type of implementation.

To link to physics, I'd say the fundamentals are signal vs noise. This can link via Shannon entropy, to a ground-up picture of entropy in relation to signal loss or uncertainty, and to a generalisation beyond two value logics (neurons for instance involve continously varying or analogue logic, & there is quantum logic)

Edited to add: Ok I see I didn't link to the context of your question explicitly, counting and errors. It is an area of the highest importance to actual professional scientists, things like measuring gravity waves wholely depended on minimising errors.

Basically, we generalise, from small groups of things where we can check, to large groups. This clearly makes you uneasy, but it's the same principle as calculus is based on, taking the limit - we find a model that as the number of elements goes up, gets more accurate. Flip a coin once, unpredictable: flip a coin 1,000 times, we can predict the mix of outcomes very well. Errors on counts are like this, count one thing, & you can be certain how many; count 1,000 things and errors get more likely; get 1,000 people to count 1,000 things, errors get less likely. We can model it, as like a pipe, what Shannon calls a channel. We know there is a true number, (usually, quantum things get weird), the actual coin flips in a specific case. It goes through the pipe, 'counting', and we find comparing many counts that there is an average - and we think that's more accurate. We also get how many people are wrong, by how much, and that tells us how accurate the counters are - like how much a data signal is degraded by going through a pipe.

We build the model, where we can check the coin flips. But mostly in life we never get to check. So we use the average of many counts, as the true answer. You are right in a way to feel uneasy, because not only does this tend to break down on small numbers, it's also very important we are modelling what kind of source of error there is, and there are different modelled distributions, but I assume you don't want that.

You ask a deep question, and on the quantum scale we never get to know the 'true' answer of linked variables at the same time, like position and momentum. That also makes many people uneasy. We live in a world full of errors & uncertainties, but that doesn't make knowledge impossible. The real problem is our intuition that 'true' always means getting to look behind the curtain - 'getting our homework marked by god'. When we think hard though, we find 'true' isn't in the 'facts', it is in the whole situation of evaluating them, and never stand separately from them.

• as much as I like that someone tried to answer this question....I didn't understand much of the answer(I am 15 yrs old)...I would much appreciate a simpler answer....Thanks btw May 15, 2021 at 9:24
• @Nerd951: Is that any clearer? May 15, 2021 at 23:57
• Oh....much clearer ......thanks a lot May 16, 2021 at 13:49
• Yup...I dont have that many reputation points to cast a vote....anyhow, the answer was ultra helpful for me...so, thanks a lot again May 19, 2021 at 5:33
• The idea of "true = signal, false = no signal" is used in Morse code. But modern digital systems use two different signal values rather than trying to reliably determine "no signal". This allows detection in the presence of noise, even for extraordinarily weak signals like from distant spacecraft. Sep 18, 2022 at 1:27