Look at the picture above. Believe it or not, that person is operating an extremely sophisticated mechanical calculator, capable of generating tables that evaluate functions called “polynomials.” Although a graphing calculator can do that, a pocket calculator certainly can’t. The device above is a mechanical purpose-built computer! This article is the next installment of my series on computing. In the previous parts, we learned about Boolean logic, the language computers think in. We then learned how to implement this logic electronically and, using our newfound understanding of electronics, how to make computer memory so that computers can record results
Mathematics
explanatory articles on math
Computer Related / logic / Mathematics / etc.
The Turing Machine
This is the sixth part in my multi-part series on computing. In the previous parts, we learned about Boolean logic, the language computers think in. We then learned how to implement this logic electronically. And finally, we learned how to make computer memory, so that computers can record results of calculations. Now before we conclude the series, we’re going to take a quick detour into computational theory and the Turing machine. Alan Turing’s Machine of the Mind In 1936, mathematician, WWII codebreaker, and all around awesome guy Alan Turing wanted to investigate a problem in formal logic. Specifically, he
Computer Related / Electronics / logic / etc.
The Boolean Circuit and Electronic Logic, Part 2
If the presence of electricity can be made visible in any part of the circuit, I see no reason why intelligence may not be transmitted instantaneously by electricity. ~Samuel Morse This is the fourth part in my multi-part series on how computers work. Computers are thinking machines, but they can’t do this on their own. We need to teach them how to think. And for this, we need a language of logic. In the first part of the series, I introduced this language of logic, Boolean algebra. In the second part, I described how to formulate complex logical statements
Computer Related / Condensed Matter / History / etc.
The Boolean Circuit and Electronic Logic, Part 1
Living in a vacuum sucks. ~Adrienne E. Gusoff This is the third part in my multi-part series on how computers work. Computers are thinking machines, but they can’t do this on their own. We need to teach them how to think. And for this, we need a language of logic. In the first part of the series, I introduced this language of logic, Boolean algebra. In the second part, I described how to formulate complex logical statements using Boolean algebra. Now, in part three, I lay the groundwork for how we can implement simple Boolean logic using electronics. In
logic / Mathematics / Science And Math
George Boole and the Language of Logic, Part 2
Anything that thinks logically can be fooled by something else that thinks at least as logically as it does. ~Douglas Adams This is the second post in a multi-part series explaining how computers work. A computer is a thinking machine, a device which applies logic to any problem we ask it to. However, computers don’t know how to do this automatically. We have to teach them. And to teach them, we need a language of logic. Last time, we introduced one such language of logic, Boolean algebra. This time, we learn how to make composite statements in Boole’s system.
abstract algebra / logic / Mathematics / etc.
George Boole and the Language of Logic, Part 1
Logic takes care of itself; all we have to do is to look and see how it does it. ~Ludwig Wittgenstein Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic. ~Lewis Carroll This is the first post in a multi-part series explaining how computers work. At its heart, a computer is a logical-thinking machine. It’s very good at starting with several assumptions and deducing a conclusion from those assumptions. Of course, a computer can’t do any of that on its own. We need to
Mathematics / probability / Science And Math
Throwing Darts for Pi
The ancient Greeks defined the number as the ratio of the circumference of a circle to its diameter. Since then we’ve discovered that is incredibly important. It appears everywhere in physics, mathematics, and engineering. But how does one calculate it? is an irrational number, so it’s impossible to calculate perfectly precisely. Nevertheless, it’s important to have an accurate approximation. The Greeks originally calculated by taking a piece of rope or twine of known length, bending it into the shape of a circle and comparing the diameter of the circle to the length of the twine. Since then, many many
Mathematics / Science And Math
Probability: Part 2 (Distributions)
Editors Note: This week, I’m busy with final exams here in Guelph, so my good friend Michael Schmidt has graciously agreed to do a guest post. Thanks, Mike! Hi everyone! Since last time I decided to talk about the basics of probability, I thought this time I would expand on that subject. In part 1, I discussed how to count different possible outcomes of random events and determine the likelihood of particular events. If you have not read that, or it’s been a while, you should read over Part 1. This method is great when where are relatively few possible
abstract algebra / History / Mathematics / etc.
International Women’s Day Spotlight: Emmy Noether
The connection between symmetries and conservation laws is one of the great discoveries of twentieth century physics . But I think very few non-experts will have heard either of it or its maker[:] Emily Noether, a great German mathematician. But it is as essential to twentieth century physics as famous ideas like the impossibility of exceeding the speed of light. It is not difficult to teach Noether’s theorem, as it is called; there is a beautiful and intuitive idea behind it. I’ve explained it every time I’ve taught introductory physics. But no textbook at this level mentions it. And
cosmology / Discrete Math / Geometry / etc.
Quantum Geometry: Causal Dynamical Triangulations
A “quantum gravity expert” is presumably someone well acquainted with the details of our immense ignorance of the subject. I suppose I count. ~John Baez I long ago promised that I would discuss some of my own research. Here’s the first post that makes good on that promise. Today I’ll discuss a theory of quantum gravity. Why Quantum Gravity? Without a doubt, the two greatest advances in physics in the last 120 years were the advent of general relativity and quantum mechanics. These two amazing theories have totally changed the way we see the world. Quantum mechanics describes the