What we're going to do next is replace all these 1's and 0's in blue with variables, unknowns, xij's. So we're introducing Boolean 01 variables. xij is going to be 1, if we've decided to pair Professor i with Class j, and 0 if we don't.
The idea that Shannon comes up with, essentially, that you can use switches as the units and symbols and operators in acting out Boolean logic, that ones and zeros can represent yeses and noes, that a series and sequence can represent ANDs and ORs, that whether or not an outcome happens, like a light turns on, could represent the IFs of Boolean logic and the outcome.
So there's a power operator-- which you see is a very similar symbol to the mathematical exponentiation, it just has a dieresis above it-- And that Boolean array can just be added to the original data.
having a mode of interconnecting these things to make the function that user requires and that is uh using Boolean algebra so you vastly simplify the user task by saying well what does the user really know how to do anyway
The way the machine works is the first thing that happens is the variable card, which I always call them address cards This is 10 years before Boole.
I started working on an advanced searching function. I designed and implemented a Boolean one. It was very primitive, and I wished for something more sophisticated, but I did not have the vision to design it, and today, search engines like you have here at Google
But he always wants to know something like, can you tell me where your demodulation juncture is? It should be near the Boolean overpass valve. And I never know where anything is.
quite unacnowledged is apparently he completed Aristotle's work in in in brilliant ways. For example, he introduced what we would call today boolean connectives and or not an exclusive or besides the implies that
And I was fortunate my mother stumbled on Smullyan's book "Alice in Puzzle-land." How many of you read "Alice in Puzzle-land?" I was going to say, there's got to be at least a couple. And that became my introduction to the field of Boolean logic, in liar-truthteller puzzles and logical paradoxes. Smullyan's use of Lewis Carroll suited the truthteller puzzles since, you know, Carroll had been a logician himself.
The binary representation of truth is so ubiquitous that we chronically logical true false and computational 1 0, on off binaries. A programming language permits me to have a Boolean variable. Let's call it is this thing on, which can be either true or false.
Bull came up with with his famous book the laws of thought. Uh where the first part of the book is the foundation of Boolean logic. The second part of the book is the foundation of probability. Uh very interestingly uh so bull uh came
Uh very interestingly uh so bull uh came up with with with uh with uh the boolean algebra and boolean calculus the propositional calculus.
of 0's and 1's. And a big part of that accomplishment was showing the connection between Boolean logic and the relays, or switches, that were part of computing systems.
So there's a power operator-- which you see is a very similar symbol to the mathematical exponentiation, it just has a dieresis above it-- So throws equals 5 returns-- well you might expect some kind of Boolean array.
You're going to get the topology of every axis, axes, axi. And once you have the axis data, all you have to do is boolean the axis. You’re going to end up with an OBJ file that’s super high quality, you can render in an infinite quality of lighting conditions.
happens, like a light turns on, could represent the IFs of Boolean logic and the outcome. So Shannon writes his great master's thesis that explains how to use these principles of Boolean logic to change circuit design so that rather than being a trial and error process that you can have a knack for, Shannon actually shows how you can dramatically simplify it and do everything that's required to construct
But at the same time, we also say that if successful companies in the economy can behave like Bell Labs, we're all better off. if you look at the two polls of his whose most famous work, you've got Boolean algebra.
open a switch and it's 0, and close it and it's 1, then by combining these, you can solve Boolean number problems. This was the first paper to say that. The concept of calculating things using Boolean number theory existed before, but around 1937, this came along and people started thinking, "Maybe we can do this with a machine? Maybe we can use this to decipher codes or calculate ballistics." It
So there's a power operator-- which you see is a very similar symbol to the mathematical exponentiation, it just has a dieresis above it-- And, in fact, APL programmers call this a Boolean array, but actually it's a 1 bit integer.
And he also says, if Bob Noyce was still alive, he'd be sharing this prize with me. Turing's papers published on universal computing, but Shannon and other people are starting to apply Boolean algebra to how to do it in circuits.
de discussion qui soient contradictoires. La question ce n'est pas tant de savoir si vous savez taper du javascript ou pas, mais c’est : quelle est la logique, le bool éen, comprendre le bouléen.
So Shannon double majors in engineering and math. And again, and other people did it, but he was sort of unique in both having that sort of abstract background in mathematical logic, and especially Boole's theory, and in the more practical engineering side of electrical engineering, which we can get into.
for each new problem. And then Shannon gets to thinking about the connections and analogies between the relays, the kind that we saw in the Theseus video and a Boolean logic. The idea that Shannon comes up with, essentially, that you can use switches as the units and symbols and operators
in acting out Boolean logic, that ones and zeros can represent yeses and noes, that a series and sequence can represent ANDs and ORs, that whether or not an outcome happens, like a light turns on, could represent the IFs of Boolean logic and the outcome. So Shannon writes his great master's thesis that explains how to use these principles of Boolean logic to change circuit design so that rather than being a trial
This is a relay circuit, and it's incredibly interesting. For example, if you open a switch and it's 0, and close it and it's 1, then by combining these, you can solve Boolean number problems. This was the first paper to say that. The concept of calculating things using Boolean number theory existed before, but around 1937,
But really, I try to get people to figure out what's behind it; it's the concept of filtering. And again, people, I worked in the computer industry, Boolean is kind of familiar to me. But if I'm sitting with folks that are in their 60's, 70's or 80's and I talk about Boolean Operators, well they're not gonna, you know, unless they
And again, people, I worked in the computer industry, Boolean is kind of familiar to me. But if I'm sitting with folks that are in their 60's, 70's or 80's and I talk about Boolean Operators, well they're not gonna, you know, unless they came from a specialized background, they're not gonna be familiar with these terms.
And some of the messages were so important that Hitler himself signed them. "And a group of Britain's leading mathematicians begin a year of desperate search. They used Bayes' rule, logic, statistics, Boolean algebra, and electronics. And they also began working, work on designing and building the first of ten Colossi, the world's first large scale electronic computers.