101–110 of 319 posts
Side question: maintenece of functional programs is easier, because you don't need to think about state. Could it be used to create a functional programming language, easily understood by non-programmers or beginners , so they too could take a program and adapt it to their needs ? Does such language exist ?
https://en.wikipedia.org/wiki/Joy_(programming_language)
(Shameless plug for my own implementation: http://joypy.osdn.io/)
I spend a lot of time listening to people ramble in meetings or troubleshooting, where I wish they understood the subject matter enough to explain it as if talking to a six year old.
Earlier quoted context omitted.
Affected? f(x) = 6 has a pretty obvious effect on all input other than 6. Your comment is more of an indictment of identity functions than dimension-losing functions.
A phrasing more to the point is that one expects the input to have some effect on the output . One usually obtains this by, colloquially speaking, performing actions on the input, since if you don't act upon the input in some way, you're going to get a constant result. Of course, you are correct in that some actions don't really do anything, but they're observationally indistinguishable from not acting on the input i…
If you don't act on the input, you have an identity function, not a constant function. Constant functions must alter their input whenever it doesn't match the constant output. Nobody ever complained that the problem with Procrustes was that he didn't do anything to the guests in his bed.
And in the other direction, I don't understand why you want to characterize "multiply the input by zero" as an action that "doesn't do anything"? In what sense would that be true?
This is fantastic. Reminds me of Hofstadter's conversations between Achilles and a Tortoise. The trouble with most math I've encountered isn't the concepts, it's the quality of the abstractions we use to represent and interpret them. The best(worst) example I can think of is the Alice/Bob description of cryptographic protocols, where somebody's idea of teaching is, "let's take these symbolic representations and inste…
I for one really like reading about Alice and Bob. Amongst other benefits, it helps me consider how, even if currently just a theoretical algorithm, that particular protocol could end up being used in real world communications.
Procedural thinking is something that anybody who knows socks come before shoes can do. Conditionals can be understood by anybody who wears different clothes on a weekend than on a schoolday. Loops can be understood by anybody who can eat a bowl of soup by drinking a single spoonful and then doing that again and again until the soup is gone.
Kids can definitely engage in computational thinking from a young age. We just need to offer them the opportunities to do so.
I remember that at elementary school we turned on a bunch of C16-s at the same time and we tested random number generators and some showed the same value, cool demo of determinism
instead of xλ6 I would have chosen xλ3.14159265359 it might lead to different questions, but who knows, just deeper rabbit holes :)
This is fantastic. Reminds me of Hofstadter's conversations between Achilles and a Tortoise. The trouble with most math I've encountered isn't the concepts, it's the quality of the abstractions we use to represent and interpret them. The best(worst) example I can think of is the Alice/Bob description of cryptographic protocols, where somebody's idea of teaching is, "let's take these symbolic representations and inste…
The reason that Alice and Bob are introduced is because they are different entities and each has different powers, restrictions and goals. If you want to do a correctness or security analysis of a protocol, introducing and defining these parties is hugely important and useful. Otherwise, its very easy to make mistakes about where information is in the system and how it is being manipulated. More generally, there is a philosophical approach called operationalism [1] that demands that all science theories be couched in terms of protocols so we don't make mistakes about what they say.
This game can be played in a group, too: https://en.wikipedia.org/wiki/Zendo_(game) > once the guesser thinks they know what the function does, the players switch roles and the person who came up with function specifies some inputs in order to test whether the guesser is able to produce the correct outputs. In Zendo when the guesser offers the wrong rule, the 'master' must tell them an (input,output) pair where the g…
> if 4 is prime then all numbers are prime
Is a true theorem (and things along these lines)
Cool, this sounds like a general form of the picnic game[0].
An input to the "picnic" function is a food (or other object), and the output is whether or not it can be brought to the picnic. The picnic game's hidden function that needs to be uncovered is a predicate function. E.g. if the hidden function is "Things that start with the letter A", then "apples", "anchovies", and "albatrosses" could be brought to the picnic, but not "bananas", "cameras", nor "dessert". In that example, the function would look like:
lambda x: x.firstLetter() == 'a'