At the end of last year before going away for the holidays, I laid out a miniature program for learning / teaching about rates of change. The first step was to appreciate the tremendous difference between linear and exponential change. It is easy to write down the relevant definitions: in linear growth we take the previous value and add a constant to it, whereas in exponential growth we take the previous value and multiply with a constant (that’s greater than 1 – for a constant less than 1 yo...

At the end of last year before going away for the holidays, I laid out a miniature program for learning / teaching about rates of change. The first step was to appreciate the tremendous difference between linear and exponential change. It is easy to write down the relevant definitions: in linear growth we take the previous value and add a constant to it, whereas in exponential growth we take the previous value and multiply with a constant (that’s greater than 1 – for a constant less than 1 yo...

Last year’s Tech Tuesday ended with a first look at computational complexity. We saw how crazily long a brute force attempt to find a 40 character string would take. This was the result of exponential growth in the runtime of our algorithm. Today we will start to dig a bit deeper. Let’s consider a very common problem: checking whether a word is part of a group of words. For instance, if you use the “find on page” feature in your browser you can check if this page contains the word “freezing” ...

Last year’s Tech Tuesday ended with a first look at computational complexity. We saw how crazily long a brute force attempt to find a 40 character string would take. This was the result of exponential growth in the runtime of our algorithm. Today we will start to dig a bit deeper. Let’s consider a very common problem: checking whether a word is part of a group of words. For instance, if you use the “find on page” feature in your browser you can check if this page contains the word “freezing” ...

This will most likely be my last blog post for the year. I am planning to take off a couple weeks not just from writing but also from spending pretty much any time online. During this time I look forward to reading a number of books that have piled up in my queue (both non-fiction and fiction – thanks for the many recommendations in comments here and on Twitter). I have taken breaks like this several times before and have always felt refreshed by them. In addition to the normal changes I will...

This will most likely be my last blog post for the year. I am planning to take off a couple weeks not just from writing but also from spending pretty much any time online. During this time I look forward to reading a number of books that have piled up in my queue (both non-fiction and fiction – thanks for the many recommendations in comments here and on Twitter). I have taken breaks like this several times before and have always felt refreshed by them. In addition to the normal changes I will...

Belated Happy New Year everyone. Today I am traveling back to New York – weather and air traffic permitting – after a great family ski vacation in Colorado. As announced at the end of last year I took a break from (most) email and also largely from social media, other than occasionally looking at Twitter. The net result was that I had time to read several books, including the wonderful Age of Wonder (thanks to Ed Cooke who gave me a copy), Abundance, much delayed Guns, Germs and Steel, and an...

Belated Happy New Year everyone. Today I am traveling back to New York – weather and air traffic permitting – after a great family ski vacation in Colorado. As announced at the end of last year I took a break from (most) email and also largely from social media, other than occasionally looking at Twitter. The net result was that I had time to read several books, including the wonderful Age of Wonder (thanks to Ed Cooke who gave me a copy), Abundance, much delayed Guns, Germs and Steel, and an...

I am sympathetic to Uber’s basic argument that surge pricing is the market at work as (a) nobody is being forced to take an Uber and (b) raising prices puts more Ubers out on the street. On Saturday evening, close to the height of the storm I had to go to the Upper East Side to pick up one of our kids. I quickly decided to take the subway which was running on time and only cost $2.50 each way, even though that meant I had to walk about a dozen blocks in the storm. As an avid skier and lover o...

I am sympathetic to Uber’s basic argument that surge pricing is the market at work as (a) nobody is being forced to take an Uber and (b) raising prices puts more Ubers out on the street. On Saturday evening, close to the height of the storm I had to go to the Upper East Side to pick up one of our kids. I quickly decided to take the subway which was running on time and only cost $2.50 each way, even though that meant I had to walk about a dozen blocks in the storm. As an avid skier and lover o...

In case you come here only on Wednesdays when I write about homeschooling, you might also want to check out Tech Tuesdays (a series that goes back several years). In yesterday’s Tech Tuesday I wrote about computational complexity and gave an example of a program that would take hundreds of thousands of years to run. It turns out to have been an example of exponential growth which happens to, well, grow a lot! That reminded me that I have been meaning to write about rates of change more genera...

In case you come here only on Wednesdays when I write about homeschooling, you might also want to check out Tech Tuesdays (a series that goes back several years). In yesterday’s Tech Tuesday I wrote about computational complexity and gave an example of a program that would take hundreds of thousands of years to run. It turns out to have been an example of exponential growth which happens to, well, grow a lot! That reminded me that I have been meaning to write about rates of change more genera...

So far in the Tech Tuesday series on the theory of computer science we have covered questions of computability. We have looked at ways of formalizing computation through abstract machines such as the Finite State Machine and the Turing Machine to explore limits on what can be computed at all. We saw with the Halting Problem that the power to compute lots of things is gained at the cost of not being able to say much about the computation (e.g. will it stop?). Now we will turn our attention to ...

So far in the Tech Tuesday series on the theory of computer science we have covered questions of computability. We have looked at ways of formalizing computation through abstract machines such as the Finite State Machine and the Turing Machine to explore limits on what can be computed at all. We saw with the Halting Problem that the power to compute lots of things is gained at the cost of not being able to say much about the computation (e.g. will it stop?). Now we will turn our attention to ...

A couple of weeks ago I wrote a post on bitcoin as protocol that got a couple of hundred comments from which I learned a lot. This is an important topic and Chris Dixon has done a lot of good thinking and writing on this. He has a new short post on the relationship between Bitcoin and the Byzantine Generals problem. Chris wrote this mostly as a reaction to various New York Times coverage of Bitcoin which so far misses the protocol innovation. While I agree with Chris, here are some (possibly ...

A couple of weeks ago I wrote a post on bitcoin as protocol that got a couple of hundred comments from which I learned a lot. This is an important topic and Chris Dixon has done a lot of good thinking and writing on this. He has a new short post on the relationship between Bitcoin and the Byzantine Generals problem. Chris wrote this mostly as a reaction to various New York Times coverage of Bitcoin which so far misses the protocol innovation. While I agree with Chris, here are some (possibly ...

On Monday I posted about looking for a Research Assistant primarily to look into questions around using Basic Income Guarantees as a way to deal with what I believe is the end of work as we know it. Then yesterday Fred wrote a terrific post on the Limits of Capitalism and linked to my earlier post driving more traffic to it. The net result is that I now have many wonderful folks interested in helping out and will be sorting through that over the weekend. In the meantime though I wanted to add...

On Monday I posted about looking for a Research Assistant primarily to look into questions around using Basic Income Guarantees as a way to deal with what I believe is the end of work as we know it. Then yesterday Fred wrote a terrific post on the Limits of Capitalism and linked to my earlier post driving more traffic to it. The net result is that I now have many wonderful folks interested in helping out and will be sorting through that over the weekend. In the meantime though I wanted to add...

There is an amazing tool out there for teaching and learning about Math (and the world) and not enough people know about it. If you have never tried it out before, you should head over to Wolfram Alpha right now. Wolfram Alpha describes itself as a computational knowledge engine which may not mean much to people and the sparse home page with just a search box doesn’t help if you have never heard of it before. But as a starter you could think of it as the intersection of the world’s best graph...

There is an amazing tool out there for teaching and learning about Math (and the world) and not enough people know about it. If you have never tried it out before, you should head over to Wolfram Alpha right now. Wolfram Alpha describes itself as a computational knowledge engine which may not mean much to people and the sparse home page with just a search box doesn’t help if you have never heard of it before. But as a starter you could think of it as the intersection of the world’s best graph...