Sorry for going so quiet.
Today I took the stupid O’clock train from Braga to Lisbon, actually managed to tick off some of to so list and went to ArXiv to see if there were any new papers I should be aware of. After “Functional Analysis”, I clicked “GM”. This may have been unwise.
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Some songs from home for the tough times, from the Specials and the Streets
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First- and second- year undergrads often think that proof by induction* is extremely hard, even if they can actually do it without thinking. More than once I’ve had conversations with a student along these lines:
MJH- So what’s the problem?
Undergrad – I can see that this result is true but I don’t know how to prove it.
MJH – OK, why is true?
UG – Well it’s trivial if n=1, and [something simple] means that shows we have when n=2 and [the same simple thing] means we can get n=3 and keep repeating up to any number.
MJH – Exactly. That’s why it’s true.
UG – So how do I write that out?
MJH – Well it’s a basic induction. Write it out like all the examples of induction.
UG – INDUCTION!? I don’t know how to do proof by induction. It’s hard!
MJH- ARGH! You just did!!!one
So anyway, maths undergrads reading this, you can do induction. Well done. Good. Let’s do induction on strings of the word “buffalo”.
The single best title of any article on Wikipedia is Buffalo buffalo Buffalo buffalo buffalo buffalo Buffalo buffalo
. The notable thing about this string of “buffalo” is that it can be parsed as a sentence. This fact was first noted by the computational linguist William Rapaport of (naturally) the University of Buffalo. We use the facts that:
“buffalo” is a plural noun (1 buffalo, 2 buffalo,…);
“to buffalo” is a (somewhat rare) verb meaning “to bully”;
“Buffalo” is a city in the American state of New York and in English we may use city names as adjectives (e.g. “the London mayor is a laughing stock”).
This lets us parse the sentence as follows (this is taken form Wikipedia).
[Those] (Buffalo buffalo) [whom] (Buffalo buffalo buffalo) buffalo (Buffalo buffalo).
THE buffalo FROM Buffalo WHO ARE buffaloed BY buffalo FROM Buffalo ALSO buffalo THE buffalo FROM Buffalo.
. OK, but what does that have to do with proof by induction? Well we claim that, for each natural number n, we can repeat the word “buffalo” n times and then (give or take capitalisation) parse it as a sentence**.
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I’ve had a decidedly ungood Friday. Made the mistake of going to office. Network borked. Then I got lost in an underground car park (no I don’t drive don’t ask).
Anyway the “proper” understandings of what the holiday is held to mark always left me bit cold but Woody’s version connects for me.
The “top searches” for this blog
matt heath, marcus du sautoy gay, (s + c) x (b + f)/t – v, where s = overall shape (“including tendency to droop”), c = circularity, b = bounce factor (not to be confused with “wobble”), f = firmness (with perfect being “like a comfy bed”), t = skin texture and v = vertical ratio (the goal: “on the top-heavy side of symmetrical”). for the male rear end, the equation replaces bounce, circularity and vertical ratio with m (muscularity), l (leanness) and o (overall symmetry), listen number, immigrant expatriate
This amused me slightly. Of course now I’ll attract people searching for these even more.
I was starting to think it was some kind of vapourware, but the Tricki is up to view (via Tim Gowers ). You can’t edit yet, and it’s small. The articles there at the moment are well written (when they are complete).
I hope the project works. The sort of information that it is designed to contain is not easily available anywhere else. It’s the nature of maths that you can give a completely convincing explanation of why something is true (a proof) without giving away very much at all about how you came to know it was true (the endless headdesking before the proof). AFAIK there is no other field of study where this is true to anything like the same extent. For better or worse, the normal style of a maths journal paper positively encourages hiding the process that lead you to the result. Thus, the only way you can usually find out tools for proof is by having somebody show you, and it’s obviously rather hit-and-miss as to whether you will ever explain your problem to the person with the right trick up their sleeve. Somewhere to pool this sort of information and a decent way of navigating it will be very useful indeed.
I also think it has a fairly good chance of working well. I can see possible problems; it would be hard (and probably counter-productive) to set down very firm rules about how articles should be( such as exist at Wikipedia) s conflict resolution will rely on people being reasonable. I think this won’t be too bad though because (IME and compared to academics in other disciplines) mathematicians have, typically, as a group, fairly good habits with respect collaboration.
3. What do you get if you add two ODD numbers together? – an even number
4. Do you think this is always true? – yes
5. Why do you think so? My MoM Said So
The question is what she could possibly be expected to have put that would be better. Could a child so young be taught even a vague understanding of a better reason? Some informal “first draft” of what a proof is? Is it worth the effort to try?
On a side note, sorry for the not posting for a while.
Well maybe it’s just being a mathematician in the United States that’s great. Not just great, in fact, but the best job in America according to a study by a job search website.
Well I like my job, but I was a bit surprised by this. Then I saw that the methodology is ridiculously arbitrary . Physical exercise is intrinsically bad? I knew there was a reason nobody wanted to be a professional footballer. Apparently meeting the public is also very bad. Yeah, people suck don’t they?
Basically, according to this survey mathematician is the best job available but only because there isn’t full time employment available as the subject in an experiment on sensory deprivation (a job that would actually share many of the downsides of mathematics but would lack the cycles of manic optimism and crushing disappointment).
Oh and $94,160? That’s Zimbabwean dollars, right?
Hat tip to Edge of the American West (who are historians and philosophers amongst other things; pwned!)
I can see absolutely no flaw in the following argument by Daryl McCullough.
My complaint about rephrasing Godel’s result as saying that the Godel sentence G can neither be proved nor disproved is that, to me, the ontological status of “G cannot be proved” is *exactly* the same as the status of “G is true”. To say that G is true is to say that there does not exist a natural number satisfying such and such a property. To say that G cannot be proved is to say that there does not exist a proof satisfying such and such a property. I don’t see how the latter makes any less ontological commitment than the former.
GARGH! Thus (unless someone can furnish me with a reason why it may be wrong) I probably going to have to accept that there isn’t really a good reason not to say “true”. After all there is no alternative rendering that avoids the same potential confusions and we don’t expect popularisations to define things perfectly – just to give the “shape” of the idea, so any confusion between a technical use of “true” and an everyday one is acceptable (they are different but close enough to get some understanding – it’s not like “group”).
It still seems squicky to me but I guess that’s my problem.