This is a lie, column H in the spreadsheet listed by you clearly shows it to be a calculation. Raw data means the quantities were just as recorded with no calculations, the direct observed physical quantity recorded.
You are right; cut per stroke is a calculated quantity. My bad.
Ok this is a prefectly valid challenge. Now I ask you the following question, if you accept that they are two different physical quantities, then you also accept that they will behave differently? Now don't you see an obvious problem with a knife which is blunting by slicing and you are quantifing the rate of blunting (loss of sharpness) by measuring the wrong type of sharpness?
Because every model I have seen supported by data shows push cutting sharpness to be a strong function of edge width or edge radius. And the means chosen in our work to increase the edge radius is, in my opinion, a reasonable representation of typical uses of hunting knives.
There is not a mathematical basis for my assertion, because I have not provided any correlation or other mathematical proof. However, I am aware of no mathematical basis for denying the assertion, because I am aware of no mathematical data that proves a lack of correlation.
You have asserted that Buck's experience with Ionfusion blades is mathematical evidence. I'm not aware of Buck's experience, and asked you to provide a reference, since you are. But you seem to be unwilling to.
I have already mentioned, both in the
paper and on the forum, that I don't believe CATRA ERT media provides results representative of typical human use, because of the embedded silica. So having the CATRA ERT test be poorly correlated with human use is not surprising to me.
It was you who made the assertion that machine testing can't be valid for defining human performance. Since I've not seen any data supporting this claim (just an allusion to a Buck test with different wear media), I repeat that we have a difference of opinion here. It's just opinion. Neither one of us has provided math or physics supporting our positions. Neither one of us has supported data. And I believe my opinion ought to carry as much weight as yours, although you're free to disagree.
I gave you two examples and one is public the other one will be shortly. Plus I find it completely unreasonable that you actually contend this because it shows a complete lack of understanding of even basic physics and general issues of biomechanics. Plus like I said this has been known and published in german for over 50 years, you really think I just made up all those references. That is just absurd.
No, you didn't give me two examples. You referred to two examples in general terms, when I asked for mathematics. You assert it's all mathematics. I haven't seen the mathematics. I asked for a reference; you gave a vague answer. I'm still waiting for mathematical proof, not just reference to authority (e.g. everybody knows, the germans knew it for 50 years, if you had any knowledge of physics you'd know). If it really is math, please just show me the math. I think I've demonstrated the ability to understand your math, even when you try not to explain it clearly.
This is again actually unreasonable because the burden of proof is on you to actually prove the correlation. But as I have noted examples of where it fails. Buck admitted this publically and noted that they had to stop and switch to human testing because the CATRA results were meaningless on the Ionfusion blades. Now there is no way you can't figure out why and realize that is a huge systematic bias in general. You have to be trolling here.
I clearly have a burden of proof if I want to assert that there is correlation. I have not asserted there is correlation. I have clearly stated that it is my opinion that there is correlation, but it's not proven mathematically.
However, you assert a "huge systematic bias in general", and assert that it's based in math and physics. So I'm still waiting for a mathematical demonstration of the "huge" bias you contend exists.
I have in fact shown many times how the same principle makes comments like "I have cut nails in half with XXX knife with no damage." completely meaningless. Again, this is all first year physics, nothing advanced. There is no way anyone with any level of engineering background would not see this as perfectly obvious. Plus anyone who used a knife would know the problem right away. It has in fact been described as a problem on the forums for years (the same concept I mean). So all serious knife users are aware of it.
Exactly what principle are you referring to here? Is it a fundamental physics principle? A fundamental mathematics principle? If so, it will probably have a name, like "conservation of energy", or "Newton's first law", or "the fundamental theorem of algebra". If you will explain what the principle is, then we can have a discussion about whether it applies to this situation.
As far as I know, many serious knife users on the forum place great stock in rope cutting tests like Wayne Goddard's. When I read Blade magazine, it's standard for knife reviewers to test cutting ability by cutting hemp rope. On your
sharpness review page you refer to rope slicing tests that are generally accepted. On the basis of these tests, I believe the physics of cutting rope to be generally similar to the physics of general use for a hunting knife, although I can't prove it mathematically.
I stated a difference function, it was perfectly valid as are all transformations within their domains. It will however blow up the noise as I noted. Difference functions are also not used when the data noise is low but when the noise is low compared to the difference. Otherwise your slope function will be undefined and just oscillate about zero.
So you agree that difference functions are used when the noise is low compared to the difference. I think that's just what I said, but with an additional qualification.
No it isn't a subjective choice. Really, that is how you see chosing statistical and numerical methods? Wow, that is one of the worst interpretations I have seen in regards to numerical analysis. This is all supposed to be defined using math, even the choice of something as simple as to include or not include a data point in the analysis. It isn't subjective at all.
Would you point me to a single reference where somebody who is a recognized authority on Numerical Methods, other than Cliff Stamp, says that the choice of numerical method to apply to a problem is defined by first principles?
I don't believe you can find one. In applying numerical methods, there is almost always more than one way to perform a numerical calculation. Some are more precise than others; some take longer than others. Some work well with one kind of data; others with other kinds of data. As an example of this, you can refer to
Numerical Recipes, Section 4.6 on multidimensional integration, where they describe the tradeoffs to be made in determining the integration method.
The calculations on the raw data to produce the plot. Manipulation is likely a poor choice because you seem to think it implies improper behavior. It can, but that wasn't how I meant it there. Transformation would have been a better term. As a simple example, consider this transformation :
f'(x_n)=f(x_n+1)-f(x_n)
THis is a well known transformation and it will EXPLODE noise and would never be done on experimental data. You would model the base data and transform the coefficients if required. This is all really basic modeling procedure.
Because the model assumes something and you don't need to. It shows you exactly what the data says with no assumptions on behavior and allows you to calculate the uncertainty in the ratios directly from the uncertainty in the data. From the models you would have to do a fairly complex calculation on the parameters, uncertainties and correlation coefficients and quality of fit and this would only be valid if the model is true. From the data there is no if, that is just what it shows directly.
Cliff, you can't have it both ways. It's either better to model the data before the transformation, or to do the transformation before the modeling. Or, alternatively, if sometimes you should model first, and other times you should transform first, then you need to admit that there are choices to be made. And if you can't give me specific mathematical reasons (which should include the results of calculations on the data), then in my opinion you're admitting that there is a subjective component when deciding how to transform the data to derive meaning from it.
Carl
