How random is a real? Given two reals, which is more random? How should we even try to quantify these questions, and how do various choices of measurement relate? 105 more words

## Tags » Computability

#### Failing software - again

The line above is from a real (and current at time-of-posting) job advertisement for a software developer. I’m not positing it because I think it is bad, shocking or dangerous, but mainly because it is illustrative of the real world: developers are expected to be “pragmatic” when it comes to testing the software they make for correctness. 463 more words

#### Guessing Game & Non-computability

```
#include <stdio.h>
int main(){
int n;
printf("==== Guessing Game ====\n\n");
printf("RULE:\n");
printf("1. You guess a number, either 0 or 1.\n");
printf("2. then I will tell you the correct number.\n\n");
printf("Please make a guess 0 or 1:\n");
scanf("%d", &n);
printf("The correct number is %d.\n", !n);
}
… 66 more words
```

#### Not all numbers are computable

When we hear the word number, symbols like 1,,¼, π (area enclosed by a unit circle), ι (symbol for ), ε (infinitesimal), ω (ordinal infinity), ℵ (cardinal infinity), …. 173 more words

#### A Proof Of The Halting Theorem

*Toward teaching computability and complexity simultaneously*

Wilhelm Ackermann was a mathematician best known for work in constructive aspects of logic. The… 1,007 more words

#### Hector Zenil

I’ve run across some of his work before, but I ran into some new material by Hector Zenil that will likely interest those following information theory, complexity, and computer science here. 482 more words

#### Knowledge and Total Functions

In the article SKETCH OF A PROOF: COMPUTABLE TOTAL FUNCTIONS ARE NOT ENUMERABLE I have used the notion of “total functions”. What is so special about “total functions”? 752 more words