So any underscore at all makes it a symbolic variable? (Or trailing/leading underscores only?) And the name of the variable on the right-hand side of the substitution is that name with the (or all?) underscore removed? It seems very clunky, so I think I'm missing something.
Mathematica doesn’t allow underscores in names. I also think the use of _x is an error in this article (disclaimer: I haven’t used mathematics in decades)
So is the right interpretation to think of "_" not as part of the variable name at all but rather as a unary operator (that acts on its left) which denotes a variable as unbound?
It's not really an operator, it's part of a pattern-matching syntax. "_" is called Blank and matches anything. Putting a name in front of it just makes it available by name -- like referring to capture groups in a regex.
So when you call a function on some argument or list of arguments, the interpreter looks up all the function definitions and finds one with a pattern that matches.
Double[x_] := 2 * x
Will work for Double[3] but not for Double[3, 2], the latter doesn't match any patterns, and the interpreter doesn't know what to do with it. You would have to define another function with the same name to handle other patterns, like overloading in C++
You can further constrain the pattern to types like this:
Double[x_Integer] := 2 * x
And now the pattern only matches integers.
More in the manual, "Patterns"[0] and "More about Patterns"[1]
I don't. For one, it's broken on Android (figures floating over text, lines cut in half etc.). But the worst flaw is in the way they made scrolling change the 2D polygon: if you leave the scroll bar in some positions, it no longer actually shows a regular polygon. For a math text that's a deadly sin.
Android aside, the flaw with scrolling caught me initially, but once you get your head around it, it is actually a very intuitive way of illustrating the points being made.
It's not just the 2D polygon, all of the illustrations use the same technique. The gradient descent works especially well.
Yes, the same could be achieved with a slider, but I personally don't think I'd have tried it when scanning through.
I'm not condoning this technique for general use..
Just like precision without accuracy, but if you get accuracy you know you have a problem, but with only precision you are hopelessly misled.
If it was a strict trade-off, I would agree that the answer was somewhere on the middle. But it isn't. Most of the things that give you precision will also give you accuracy. The few things that let you exchange one for the other look too much like cheating, and seem to always have much greater impacts on accuracy than on precision.
> Most of the things that give you precision will also give you accuracy.
This is absolutely false - digital clocks are a common example. Precise to the second (or millisecond, or more!) but only as accurate as their setting.
Calculations also give precision without accuracy, like my package of tortilla chips - 13oz (368.5g) They took a measurement or specification precise to the ounce, multiplied by 28.3495, and got 368.5.
Accuracy and precision are independent variables, and the utility of either is usually limited to the order of magnitude of the other. With either "accurate to the second with a precision of milliseconds", or "accurate to the millisecond with precision to the second", you should only report a measurement to the second (or possibly a more precise measurement with an error range).
Do they have different meaning to you? They are the same thing unless there is some scientific meaning that makes them different of which I'm not aware. i.e. Theory in Science means a different thing than what it means to a layman person.
Precision is how fine a measurement is (i.e. being able to measure temperature to thousandths of degrees versus tenths), whereas accuracy is a measure of how closely your results much the objective truth. So you may have a very precise thermometer that measures to thousandths of degrees but it may not be accurate because it's calibrated such that it always reads exactly two degrees higher than it should. Meanwhile a thermometer that can only measure to a tenth of a degree is more accurate and less precise than the one just mentioned if the shown figures reflect the true temperature.
In common usage, these words mean the same thing, but scientists often give words specific meanings in order to make their research and ideas less ambiguous.
Definitions are even more important in non-scientific fields such as philosophy or math where meaningful reasoning of abstract structures and ideas would be next to impossible without giving them concrete definitions and stating your assumptions.
Remember that definitions are arbitrary, so to understand an author's argument or idea, you must seek out the author's definitions.
Hopefully that clarifies some of the discussion going on in the comments here.
I get it, these are specific definitions within a given field. I looked at the definition of both precision [1] and accurate [2] and each would use the other as a synonym, which made it a bit confusing as to what he was talking about.
[1] pre·ci·sion:
noun
the quality, condition, or fact of being exact and accurate.
[2]ac·cu·rate
(of information, measurements, statistics, etc.) correct in all details; exact.
"accurate information about the illness is essential"
synonyms: correct, precise, exact, right, error-free, perfect; More
Standard English dictionaries often don't have the precise definitions used in specific fields, which only leads to more confusion for laymen, but any good introductory Chemistry lab textbook should be able to get you up to speed on experimental science definitions.
