A physics engine, and a verification tool enforced on top of it. PhysWall inverts a closed, published, non-linear physical law at a single measurement point — and refuses when the inverse is not unique. Seven laws, one engine, and the same refusal in all of them.
A model answers whatever you ask, including questions your numbers cannot settle. This checks which of the two you had.
The two quantities a certificate can carry are not the same: a standard uncertainty is one standard deviation, and an expanded uncertainty is that multiplied by a coverage factor — usually k=2, for about 95%. JCGM 100:2008 (the GUM) requires the factor to be stated. Comparing one against the other is comparing two different things.
Three things, and each is a question people rarely think to ask:
does a stated total follow from its own numbers do two results really disagree, or only look like it did one thing get counted twice
It asks a few questions first, so the boxes make sense when you reach them, and it will tell you when you do not have enough to check anything. That is a finding rather than a failure — it says exactly what to go and ask for.
A model computes anything you give it, and computes it correctly. What it will not do is tell you the question had no single answer — because you did not ask that, and it answers what you ask.
you ask "what is the average of these?"
it answers correctly
what neither whether the stated average follows
of you asked from those numbers, and whether two
entries are the same thing twice
Bring the same numbers you gave the model. If they come back clean, that is one more reason to trust the answer you already had. If they do not, you know which part to go back to.
A model will compute anything you give it, and compute it correctly. What it will not do is tell you the question had no single answer — because you did not ask that, and it answers what you ask.
you ask "what is the average of these?"
it answers correctly
you ask "is this budget sound?"
it answers correctly, on the numbers
what neither whether the stated average follows
of you asked from those numbers, and whether two
of the entries are the same thing
counted twice
Three checks, and each one is a question a person rarely thinks to ask:
does the total follow from its parts do these two results really disagree, or only look like it did one thing get counted twice
Bring the same numbers you gave the model. If they come back clean, you have one more reason to trust the answer you already had. If they do not, you know which part to go back to.
Most people do not arrive thinking about a number. They arrive holding something — a report, an invoice, a lab result, a summary at the bottom of a page — and wondering whether to trust it.
The number is the part somebody put in front of you as the result. Usually one figure, often at the end, sometimes the only thing anyone reads:
"the average was 4.2" "total: 8,910" "we measured 100.3, plus or minus 0.2" "3 of the 5 samples passed" "efficiency came out at 61%"
If somebody handed you one of those and you cannot reproduce it from what you were also given, that is exactly the situation here.
⚠ Not whether the number is true. Nothing can tell you that from the number alone, and anyone who says otherwise is selling something.
Only whether it holds together: whether a stated total follows from the parts you were shown, whether two results really disagree, whether one thing got counted twice. Small questions — and they are the ones nobody checks.
None of these needs a formula, and none of them is unusual. They are all cases where the arithmetic was correct and the answer was still wrong.
the statement lists
building insurance 840
lift maintenance 310
cleaning 450
insurance (buildings) 840
total charged 2,440
The addition is right. Two lines are the same policy under two names, and the total should be 1,600. You cannot see this in the numbers — only in where each line came from, which is why nobody catches it.
five test scores
72 68 91 68 72
report says: average 76
They average 74.2. Everything the report concludes from 76 carries that difference, however carefully it was reasoned. This is the same shape as a published measurement guide that stated an average its own five readings did not give — and survived twenty-six years.
builder A 18,000, "give or take about 2,000" builder B 23,000, "give or take about 1,500"
They differ by 5,000, and their ranges do not overlap — so this is a real disagreement rather than two people estimating loosely. But it does not tell you which one is wrong. Either A has underestimated the work, or B has priced in something A has not seen. One more quote separates them; arguing with either does not.
gross 9,400 tax -1,880 pension -470 pension contribution -470 net paid 6,580
The subtraction is correct. The pension appears twice, and the net should be 7,050. A person checking the arithmetic finds nothing wrong, because there is nothing wrong with the arithmetic.
⚠ The maths is already in all of these. It is not advanced and it is not hidden — it is just that nobody runs it, because the document looks finished and recomputing a number somebody handed you feels like doubting them.
A calculator takes numbers and returns a number. It always has an answer, and it has no way to tell you that your question did not have one.
What runs underneath this page is a physics engine. It was built to take a measurement and work backwards to the quantity behind it — the angle a beam passed through, the loss in a conductor, the flow in a river — and to refuse when the measurement does not settle it.
Two different situations can produce the same reading. Physics has a name for it — a degeneracy — and a known way out: you add an independent observation. Not another look at the same number.
Everything on this page is that same rule with the vocabulary removed:
a total that does not follow from
its parts the parts are the independent
observation
two results that the plus-minus is what decides
disagree whether they really do
one thing counted the source is what tells them
twice apart -- the numbers cannot
A calculator that refused would be broken. An engine that refuses is working — it has found that what you gave it supports two answers, and it will not pick one on your behalf.
The same engine runs eight other tools on this site, across seven published physical laws. Nothing here was measured by us, and the same refusal appears in all of them.
Not clever. Useful.
If you do not have what a check needs, this will not simply tell you so and stop. It will say where that sort of thing usually sits, and give you a sentence to send to whoever has it — because knowing you are missing something is not the same as knowing how to get it.
And if none of the three checks fits what you have, it says that too. A tool that always finds something to say is a tool you cannot rely on when it does say something.
The first example is a real case. EA-4/02, the European guide to measurement uncertainty, has a worked example whose five readings average −92 while the document states −94. Every calculation below that line is correct, and we recomputed all seven of them.
It is the example commercial calibration software validates against, and it survived twenty-six years — because nobody recomputes a number they were handed.
⚠ That finding holds for that one document and does not carry over to measurement guides in general. A newer edition of the same guide prints readings that do average −94 — the numbers were corrected to match the figure. One worked example being wrong says nothing about the next one, and this page checks the arithmetic in front of it rather than trusting any source.
⚠ Nothing on this page was measured by us. The guide is published, the arithmetic is yours to repeat, and the tool stores nothing you type.
PhysWall was developed and architected by Gadi Zion.
Built on PhysWall — the same engine reads antenna bandwidth, conductor loss, bit erasure and heat limits. It answers what the measurement implies, and refuses when the measurement cannot say.⚠ Check this instead of believing it. Every number here reproduces from a source that is named, and the claims that turned out wrong are still printed next to what replaced them. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. How to check each one →