Although titled "blog", this is more just random rants and streams of consciousness, touching on math, juggling, programming, user interaction, business, and anything that comes to mind. Read at your peril!
Not the four-dimensional cube sort of Tesseract, this is the Optical Character Recognition (OCR) "Tesseract", software that takes an image of some lettering and produces a plain text file containing the text. Or not. It's well-known that this is "Actually Quite Hard(tm)" and Tesseract does a pretty good job "Out of the Box" with very little messing about. But the other day I ran across something…
I mentioned when talking about an oddity in vim that the behaviour of the command " J" didn't match my mental model. Sometimes software does that, it had behaviour that's totally reasonable when you think about it one way, but there's another way of thinking that causes you to be surprised. Here's another, as reported to me by a friend.
I'm going to tell you a story, so this is quite a long post. If you'd like to skip the story get directly to the main point then feel free to do so. But if you're interested in the story, make sure you're sitting comfortably, and I'll tell you how I found an oddity in /vim./
For some of my readers, this will all be completely mysterious. But for others, part way through they will go "I recognise this!" So I'd really like to hear from you ... if you recognise this, at which point did the penny drop? I'd also really like to know if you think this is obvious, and possibly even if you've seen it before. Consider the following algorithm. I'll work through an example. I'll…
Recently, Rachel and I have been watching the episodes of "The Adventures of Paddington Bear" that have been transmitted on broadcast TV here in the UK. It's not exactly gentle viewing, but Paddington is kind, helpful (or tries to be), and it always turns out well. Not very realistic, but if you watch with the right attitude, it is uplifting. Judge us if you will - we don't care.
"When you lose weight, where does it go?" An interesting question, and one where most people haven't thought about it, don't know, and really don't care. But when I was asked, it set in motion a train of thought. Follow along, and see if it makes sense.
Before you react to the title, and before you guess where this is going and form a reaction, pause. I might not be about to say what you expect. Of course, I might, but I might not, and I'd ask you to wait a bit.
Second Saturday of the month, and that means the Farmers' Market is on. Even in this second lockdown it will be running, with a one-way system and limited numbers permitted inside at any one time. But is it at the usual time? Let's check the email. Oh, I seem to have deleted it. Never mind, there will be a backup ...
Some time ago I wrote a post on Thinking About Recursion, and more recently I wrote about a problem concerning the problem of the number of Vertices Required For Cycles. As it happens, the code for that problem is heavily recursive, and provides a great example of using recursion to solve a real problem.
A few weeks ago Chris Purcell (@ccppurcell@mathstodon.xyz) said: Let a_n be the size of the smallest graph with exactly n cycles. (The first few terms are: 3, 5, 4, 6, ...) The first few values are easy enough to compute, but it gets quite tricky quite quickly. How can one construct a (simple undirected) graph with exactly 5 cycles?
The machine wouldn't read my credit card. That's not uncommon ... sometimes the contacts on my card are dirty, sometimes the contacts on the machine are dirty ... no big deal. Just lick your thumb, rub the contacts, and try again.
In late May it was becoming increasingly clear that Rachel's laptop was increasingly eccentric. A replacement would be needed, and while it wasn't yet urgent, we felt we should do something before it became so. And so the hunt began.
With the passing of Ron Graham a few people have been in touch with me to ask what "Ramsey Theory" is. So I've given a brief outline, and pointers in case people want to follow up. In truth, just stick "Ramsey Theory" into your favourite search engine and you'll get lots to follow up and chase down (as opposed, of course, to "follow down" or "chase up").
Way back in the 70s when I was building logic circuits, I was warned repeatedly that I'd have to get a few things right, or risk "locking up" or "burning out" the CMOS chips I was using. The bogeyman was "Signal Reflection", but no one could tell me what it was, or why it was so bad.
While I was writing my post on SignalReflection, I was given cause to reflect (pun intended ... sorry) on exactly the role and value of analogies in science, maths, and life in general. I've come to the conclusion that, like so many thing, analogies are neither good nor bad. They have their purpose, and each lies somewhere on a spectrum.
More than once now I've seen someone on social media using an option which has, for their purposes, been sub-optimal. In one case it led to a very unpleasant exchange, purely because one person assumed an implication that simply wasn't intended.
For those of us who love maths, it's sad to see how many people hate it, or have a phobia of it, or proudly announce "I was never very good at maths at school." The question we often counter with is "Would you be so proud of being unable to read?"
Rachel's laptop has become ... eccentric. Like a toddler, or an aging relative, who won't get up in the morning, won't go to bed at night, and won't play nicely with others, I'm afraid The Admirable Crichton has taken to not starting up properly, not shutting down properly, and occasionally just refusing to connect either over ethernet, or Wi-Fi.
It's pretty clear to most of us that skills unpractised are eventually lost. Anything at the limits of our abilities need to be exercised regularly to avoid having them waste away.
More and more often I hear people saying and see people writing "factoid", by which they mean "A Small Fact". But is that right?
Recently I was *very* surprised when a post got significant traction on a forum I visit, and I set up some tracking to see what happened ... this is the report.
Doing technically brilliant work may be enough for your personal gratification, but you should never think it's enough. If you lock yourself in a room and do the most marvellous work but don't tell anyone, then no one will know, no one will benefit, and the work will be lost. You may as well not have bothered. For the world to benefit from your work, and therefore for you to benefit fully from…
Most people are aware of the phrase: "The quick brown fox jumped over the lazy dog." But many, perhaps most, don't realise (a) Why it's interesting, and (b) It's wrong.
Software that deliberately kills the servers it is monitoring is an interesting idea. A story I read recently told of a situation where the programmer and/or engineer involved wasn't able to fix the real, underlying problem, so an overlay solution was devised that (a) worked, and (b) was feasible. This post is not about that story. This post is about a comment made by one of the readers in the…
In April 2016 my wife and I were travelling. We stayed in a reasonably comfortable but very inexpensive hotel, and meals weren't provided. As it happened, across the way was a large retail park with a large well-known supermarket chain, and they had a restaurant. We ate there four or five times, and I noticed that they were using a finite state machine.
I wrote earlier about John Conway's passing and some of my memories of him. I also mentioned there how he was once nerd-sniped by Coxeter. John didn't call it "nerd sniping" - he didn't know the term - but when I explained it, he was delighted, as it exactly matched his experience. So here is the story, as told to me by Conway at MathFest, 2015 ...
"I must have done something wrong." I hear this a lot when people are using computer interfaces. These days that's often websites, often for large corporations, and often trying to accomplish something one feels should be simple. And yet in all honesty, it's not always your fault.
John Conway has left us.
During this time of lockdown and/or self-isolation, it's tempting for those of us content with our own company to sit tight indoors and wait it out. But I'm reminding of some stories told to me by my friend Laurie Brokenshire.
A while ago Ed Southall asked a great question on Twitter about joining dots to make a parallelogram. Several people chimed in quite quickly, others took a little longer. Some were happy to have found any solution at all, others were happy to have found two solutions, and then quite a few people started to claim that there were, in fact, exactly two solutions. That made me wonder ...
I did a rough "Back of the Envelope" calculation about COVID-19. Here are my rough-and-ready results.
Last time we saw that the Axiom Of Choice seems so reasonable. It's basically saying that that the product of non-empty sets is always non-empty, and that seems obvious. But in this post we look at one of the implications of accepting the Axiom Of Choice, and wonder if perhaps it's not so obvious after all.
The first of a two-parter, here we provide a reason to accept that the Axiom of Choice is reasonable, and should be used.
Saturday, Feb 15th, 2020, and I'd delivered a Maths Masterclass just north of Cardiff in South Wales. I'd packed my things and was offered a lift to the station, which was gratefully accepted. It was raining, although not torrentially, but Storm Dennis was due to hit, and we were feeling the initial effects. This is the story of what happened next ...
Previously we looked at computing the radius of the Earth by watching the Sun coming down a building at sunrise, but there's been some question about the answer, so now let's do it "properly".
Fermat's Library on Twitter tweeted "Euler presented in his textbooks the exact formula for the volume of a sphere" and there followed an image with the actual formula. Over 12 thousand people "Liked" the tweet, but someone said: "How would you go about proving this one?" So here is how we can prove it.
In an earlier post we saw that the function f(n)=n dominates g(n)=n-ln(n), but that's no surprise. What does come as a surprise is that g dominates f. So even though for any value of n greater than 2 we already have f(n)>g(n), still we say that g dominates f. That feels *very* unexpected, and as a result you might question the value of the concept of "dominates", so we'll pause and take a moment…
Ubiquitous in mathematics is the concept of comparing things, and examining the relationships between them. Since we do that all the time and everywhere, it's worth having a look at the concept of a "Relation" in an abstract sense to try to tease out the common themes.
Last time I said: "If you do this for two different algorithms and the results are, apart from a scaling factor, pretty much the same, then the algorithms are said to have the same 'Time Complexity'." Now we'll look at that more carefully.
It's time to get our hands dirty. In this post we look carefully at a particular algorithm, and think hard about how long it takes for a given instance. From that we find an important concept emerging.
We've looked at what we mean by a "Problem", and by an "Instance" of a problem. For each challenge, we need a way of working out what the response should be. Such a method is called an "Algorithm" for that problem, so let's think carefully about algorithms.
Recently I discovered that a friend of mine, an outstandingly good mathematician, didn't know anything about how the whole "Time Complexity" thing worked, and didn't understand about $P$ versus $NP$ and similar concepts. So here is an outline of the ideas in what I hope will be bite-sized, accessible chunks.
I was given a problem recently, and I was really pleased to get the solution. I wonder if you can (a) solve it, and (b) tell me where it comes from. I've not been able to track it down at all. It's the problem of the Linear Baby Frog.
Earlier we looked at the situation of two identical cars, one doing 70, the other doing 100, slamming on their brakes at exactly the same location to avoid an obstruction. The model we used was that the two cars shed energy at a rate proportional to distance. But what if the rate energy is shed is proportional not to distance, but to time?
Some time ago I was asked about the way this website works, and as I started to explain, I realised just how much there was going on and how complicated it seemed. But they seemed to think it was neat and elegant, so I thought I'd write it up.
Supposed two identical cars are traveling along the same straight road, with one traveling at 70 kilometres an hour, the other at 100 kilometres an hour. Just as the faster car draws roughly level with the slower, they both see an obstruction in the road ahead, and (as luck would have it) at the exact same moment, exactly when they are level with each other, they both slam on the brakes.
Recently I was sent a lovely little twitchet, so I thought I'd share it for people to think about. No answers provided. Firstly, let's do something odd with the powers of two ...
Expanding on the post from earlier, and with more detail ... put "10" into a calculator and take the square root. Then again, then again, then again, and so on. Fairly quickly we get a number that's marginally larger than 1, so we can think of it as 1 plus small rubbish. But thinking carefully about the rubbish leads to some interesting results.
I'm about to go on an extended business trip, so I'm making note of broadcast TV programs that I want to record, and making sure there is enough space on the recorder. I have a large external HDD attached, so I've been transferring programs to that to make space on the internal HDD. All was going well. There's still 240 hours of space on the external HDD, so no problems anticipated. What could…
Recently someone tweeted a picture of a page from a book. It seems to be some sort a book about maths aimed at students, but in one simple paragraph there was just so much wrong, it attracted many comments from many of my friends and colleagues.