SoylentNews is people
SoylentNews
Mathematician Keith Devlin writes about how the capabilities to work with maths have changed since the late 1960s. He summarizes what he considers to be the essential skills and knowledge that people can focus on as more and more is turned over to software.
The shift began with the introduction of the digital arithmetic calculator in the 1960s, which rendered obsolete the need for humans to master the ancient art of mental arithmetical calculation. Over the succeeding decades, the scope of algorithms developed to perform mathematical procedures steadily expanded, culminating in the creation of desktop and cloud-based mathematical computation systems that can execute pretty well any mathematical procedure, solving—accurately and in a fraction of a second—any mathematical problem formulated with sufficient precision (a bar that allows in all the exam questions I and any other math student faced throughout our entire school and university careers).
So what, then, remains in mathematics that people need to master? The answer is, the set of skills required to make effective use of those powerful new (procedural) mathematical tools we can access from our smartphone. Whereas it used to be the case that humans had to master the computational skills required to carry out various mathematical procedures (adding and multiplying numbers, inverting matrices, solving polynomial equations, differentiating analytic functions, solving differential equations, etc.), what is required today is a sufficiently deep understanding of all those procedures, and the underlying concepts they are built on, in order to know when, and how, to use those digitally-implemented tools effectively, productively, and safely.
Source : What Scientific Term or Concept Ought to be More Widely Known?
(Score: 3, Informative) by Anonymous Coward on Monday February 05 2018, @06:17AM (7 children)
Read my lips: DO... NOT... TEMPT... aristarchus...
He'll show you so many facts about the wonders and limits of human cognition that you'll not be able to distill anything of value before going nuts and adopting his truth.
It will happen unless you are khallow - he's impervious to any other truth but his. And Runaway too. And TMB.
And... but enough already!!
(Score: 4, Insightful) by aristarchus on Monday February 05 2018, @07:35AM (6 children)
Too late! Georg Wilhelm Friederich Hegel said that "truth" is a rather small word, but I said it is really close to being a four-letter word. However, even though truth may be the ultimate goal of human understanding, for philosophers the beloved is mere human wisdom. And the epitome of wisdom, according to Socrates, is knowing when you do not know. This is what we need. Scientific epistemic humility. Makes the wackos look all the more ridiculous with their claims about what they know to be absolutely true! Ha!
(Score: 2) by acid andy on Monday February 05 2018, @07:46AM (5 children)
I think this is why we need axioms. We can only say if A then B but if A is our axiom then it can always be doubted. I suppose logic itself can be doubted too.
If a cat has kittens, does a rat have rittens, a bat bittens and a mat mittens?
(Score: 4, Insightful) by aristarchus on Monday February 05 2018, @08:07AM (4 children)
Of course, but only at the cost of admitted madness. Conditionals are a tricky case, and will get us into the Duhem-Quine hypothesis, but let's just say, if you say "A then B" and you admit the truth of A, then you are committed to the truth of B. And if you disagree with the reasoning, you are either lying, irrational, or both.
Take for a more simple example the "excluded middle". The classical assertion is that any proposition is either true or false, and cannot be both. Paraconsistent logics hold that the same proposition can be both, and not in the mundane sense that it is true in two different senses, which implies of course that there are two different propositions. This is either very interesting, or quite insane.
So the doubt of logic is one of those things that you have to be logical to entertain at all, but by the very fact you are entertaining the possibility, you lose the very ground for the doubt. So, not possible? One might think? Do you doubt this?
(Score: 3, Funny) by PiMuNu on Monday February 05 2018, @11:07AM (2 children)
Everything I say is false.
(Score: 4, Interesting) by aristarchus on Monday February 05 2018, @04:22PM (1 child)
True, but paradox is not the same as contradiction, not even the same as Ayer's "performative contradictions".
(Score: 5, Funny) by PiMuNu on Tuesday February 06 2018, @11:33AM
> > Everything I say is False.
> True, but paradox is not the same as contradiction
Really not true. Sorry about that.
(Score: 0) by Anonymous Coward on Monday February 05 2018, @12:13PM
Excluded middle, meet quantum mechanics.
It seems we need a sort of generalization of logic, so that we can keep our sanity.