People before tribes
The rules of Lotto 6/49 are about to change in a way that I think is pretty significant. It's drastic enough that I think we might well say Lotto 6/49 is coming to an end, being replaced by a new game that is not even properly a lotto game anymore and only happens to reuse the name.
I'm very interested in cognitive deficits: tasks it may seem human brains ought to be able to perform, but that at least some brains cannot. This time around I'd like to say a few words about mathematical foundations and the ability to understand them. The fact is that there are some questions - and they're very simple ones - that neither a human brain nor anything that functions like a human brain can answer. And understanding that fact is itself a problem that may be challenging for at least some brains.
I've posted some notes on the computer-science aspects of reporting rounded numbers in financial statements and hoping for the totals to add up correctly. You've doubtless seen footnotes on things that say "Totals may not add due to rounding." Can that be avoided? Here's a detailed examination of the question.
In which a Parable is Related and Betting Strategies are Considered
[first chapter] | [all in this series]
Aardvark: Friend Bandicoot, I heard an interesting story recently. Perhaps you might find it edifying.
Bandicoot: Oh, goody! I do like stories, Friend Aardvark.
In which there is an Inquiry into What Counts, and into the Aardvark's Commitment to the Cause
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, I've got the module passing the test suite now!
Aardvark: Really?
B: Yes.
A: And it's really the module passing the test suite, not one of your school chums hiding inside the computer?
B: Uh-huh. Well, almost.
Some Clinical Consequences of Introjection
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, I've given a lot of thought to our conversation the other day about the ontology of software engineering.
Aardvark: I had hoped you would.
B: It took me a while to see it, but I think your point about no one single test case being necessary is in fact correct.
Studies in Ontology, with a Hint of Romance
[first chapter] | [all in this series]
Aardvark: Friend Bandicoot, do you know what a formal ontology is?
Bandicoot: Yes, Friend Aardvark. I learned about them in library school.
Introducing the Mechanical Australian
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, I've implemented the double-double feature you wanted in the parser.
Aardvark: Again, Friend Bandicoot?
B: Well, you keep telling me to re-do it.
In which a Feature is Implemented, but At What Cost?
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, Friend Aardvark! I've added that extra double-double feature you wanted in the parser!
Aardvark: Really?
B: Yes!
A: Really really?
B: Of course!
A: Not just "almost," Friend Bandicoot?
In which we Accept our Limitations with Humility
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, Friend Aardvark! I've added that extra double-double feature you wanted in the parser!
Aardvark: Really?
B: Yes!
A: Really really, Friend Bandicoot?
B: Of course! Well. Almost.
A: I see.
In which a Blow is Struck for Feminist Scholarship
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, I implemented the double-double feature you wanted.
Aardvark: That's excellent, Friend Bandicoot.
B: Yes.
A: So, the test suite passes now, right?
B: Well... actually, I did something even better.
A: Oh.
In which Priorities have been Implemented
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, Friend Aardvark!
Aardvark: Good morning, Friend Bandicoot.
B: I implemented the optional extra double-double feature!
A: You mean, the module can finally add two plus two?
B: That's what I said.
In which Priorities are Set
[first chapter] | [all in this series]
Bandicoot: Good morning, Friend Aardvark!
Aardvark: Good morning, Friend Bandicoot.
B: I'm wearing my programming trousers again today.
A: I can see that you are.
B: Well?
In which a Debt is Paid
[first chapter] | [all in this series]
Post-It note on the Aardvark's office door: Home sick today. Migrane.
In which a Post-Mortem Offers Valuable Insight
[first chapter] | [all in this series]
Aardvark: Good afternoon, Friend Bandicoot. I'm sorry to be late for this meeting.
Bandicoot: That's quite all right, Friend Aardvark. Is your head feeling better?
A: No. But we need to get this module out the door anyway, so I'll go be sick some other day. I spent most of this morning going through the test suite trying to figure out what's wrong with your code, and I think I've at least got some idea -
B: But there's nothing wrong with the code. You saw me demo it yesterday.
In which a Demonstration Begins Well, and Concludes
[first chapter] | [all in this series]
Aardvark: Good morning, Friend Bandicoot. I trust you slept well?
Bandicoot: Very well, thank you, Friend Aardvark. It was most restful knowing I'd completed the project and wouldn't have to do any more work on it. Do you have new glasses today?
A: Yes, these are my demonstration spectacles.
B: Very appropriate to the occasion!
In which Concern is Expressed for One's Health
[first chapter] | [all in this series]
Aardvark: Good morning, Friend Bandicoot.
Bandicoot: Good morning, Friend Aardvark!
A: I'm surprised to see you here so early. Usually, you don't come in until just before lunch.
B: I was here all night!
In which there is No More Progress, and a Management Decision is Made
[first chapter] | [all in this series]
Aardvark: Are you almost finished with that module for evaluating expressions?
Bandicoot: Yes! I have your module for parsing strings 80% complete!
A: Friend Bandicoot...
In which there Has been a Little More Progress, but Just a Little
[first chapter] | [all in this series]
Aardvark: Friend Bandicoot, where do you stand with the expression evaluation module?
Bandicoot: I'm about 80% finished with the expression parser, Friend Aardvark. It's fun! I do like parsing.
In which Progress is Reported
[first chapter] | [all in this series]
Aardvark: Friend Bandicoot, how is that expression evaluator coming along?
Bandicoot: Oh, you mean the parser? It's about 75% complete, Friend Aardvark.
In which Some Points are Clarified, but One is Left Unanswered
[first chapter] | [all in this series]
Bandicoot: Friend Aardvark, Friend Aardvark!
Aardvark: Oh, good morning, Friend Bandicoot. I see you're wearing your programming pants again today.
B: Trousers.
A: What?
"Ah, why, ye Gods! should two and two make four?"
- Alexander Pope, "The Dunciad"
In which a Project is Initiated
Bandicoot: Good afternoon, Friend Aardvark. I trust you're well?
Aardvark: Yes, thank you, Friend Bandicoot. Are you ready to do some software engineering?
In January of 2011, I had recently arrived at the University of Manitoba to work as a postdoc with Stephane Durocher. One of the first things he asked me to do was find out how many cycles there are in an n-dimensional hypercube graph, for general n. At the time, he and I both assumed that that meant spending maybe half an hour in the library looking up the answer.
Since then it's been more than three years; thousands of lines of computer code and months of CPU time; we added two more co-authors; we didn't solve the original problem, and didn't completely solve the other problem that we ended up working on, either; but here's a journal paper, anyway, and I think it's pretty interesting. The official definitive version will be free to access until mid-December and then will go behind Elsevier's paywall; the authors' accepted manuscript on arXiv is permanently accessible.
Read the paper if you're interested in the math details; in this entry I'm going to try to tell the story behind the paper, in relatively non-mathematical terms. I'm hoping it'll be of interest to my Web log readers and give you some idea, because I often get asked this, of what I actually do at work.
To make best use of this posting, you should have a quantity of identical standard dice. Attempt to solve the questions for yourself before reading the answers. It is more fun to use real dice, but on the other hand, solving them in your head by visualizing the dice will almost certainly qualify you for membership in some pretentious organization.
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