orlylicious wrote: ↑Sun Jul 18, 2021 3:23 am
Slarti, are you sure? Realist said f(x) = 1.
<rant>
A colleague of mine once said that the best part about being a scientist is finding out that you are wrong -- it's when you learn something. But the best part about being a mathematician is knowing when you are right and when you are a scientist. In this case, I showed my work -- in other words, I proved what I said by deriving the condition for the set of solutions to the given differential equation to be a linear space, namely "(a+b)f(x) = f(x)" for all real numbers a and b. In order for that condition to be true, f(x) must be zero for all x. You don't get to argue with math - evah! If you can find a mistake in my derivation you will prove me wrong, if there is no flaw in my reasoning then I am right (alternately, if I made incorrect assumptions, say I misinterpreted Gregg's original comment due to the notational issues, then my proof is not relevant -- neither right nor wrong).
Opinions are like assholes, everyone has one and is entitled to believe whatever they wish to believe.
For an opinion to be scientific, it must be falsifiable (but not falsified) -- in other words, there must be some possible evidence that would convince you that you were wrong. A consequence of this is that there can be
NO possible evidence that would convince you that you are completely right. This is critically important because science can never give us more than an approximation of reality and all science will eventually be replaced with more accurate theories -- like general relativity and Newton's theory of gravitation.
On the other hand, math has nothing to do with opinion at all, it has to do with what can be established via rigorous logical arguments. Once something has been proven, all argument to the contrary is necessarily invalid (because proof). As a result, any mathematical description of reality (which is what science is) must have some flaw in the analogy because there is no room for falsifiability in the mathematics.
The analogy I like is the map and the territory. Reality is the territory, science is the map, and math is the language in which the map is written. There is no such thing as a 100% accurate map that tells you everything there is to know about the territory, but that doesn't mean that you can't find a map that is sufficiently accurate for navigating the territory in a wide variety of useful ways.
In the end though, it is always important to remember that the map is not the territory.
Don't even get me started about statistics...
![Towel :towel:](./images/smilies/f_towel.gif)
</rant>
p.s. This is clearly relevant to the topic at hand, as an audit should be a scientific exercise with a mathematical methodology for it to have any objective validity at all. To me, this sums up why all of these so-called "election audits" are corrosive to our democracy regardless of the outcomes.