Softball Thoughts

March 31, 2009 at 7:09 pm | In Life in America, sport | 1 Comment

Division by Zero’s spring softball season started last night with a 12-5 (or something close to that) loss. I don’t think our team has improved so it might be another long season (metaphorically anyway, it’s actually a really short season and we only play once a week).

The spring league has the interesting feature of pitching to your own team. You only get three pitches no matter where they are, so you really have to hack away. For example in my first at bat last night I had three pitches (I don’t want to blame our pitcher – he was good for the rest of the game – but this is how I saw it):
- first one was short so I left it thinking I’d get something better.
- second pitch was a bit inside and was called flat (it’s slow pitch softball so you have to get the ball above 6 feet) just as I fought it off over second base for what probably would have been a double.
- third pitch was low and away and I hit it down the first base line where it took a right turn at the base and went foul.
Then I was out! What a ridiculous game. In a real game I would have been 2-1 and feeling good.

My second time up was better – I hit a double into right center and took third on the (inevitable) throwing error. The next batter up drove me in.

My fielding still needs work. I was playing third base and made one good putout at first. But I was out of position a few times – backing up the shortstop on a ball to his right and then watching the ball instead of getting back to my base. I also have no lateral range but I don’t have a lot of hope for improving on this.

Anyway I’m hopeful that we can win a game this season but not that confident to be honest.

Earth Hour

March 29, 2009 at 8:56 am | In Life in America | 1 Comment

So I celebrated Earth Hour by playing Scattergories in the dark. It was rather difficult to read the categories. Still, I guess we were saving the world…

Calculus without limits

March 26, 2009 at 9:59 pm | In Mathematics, Teaching | 13 Comments

or: my descent into crackpottery

So I am quite unhappy with the foundations of calculus as it’s currently taught, in particular with how complicated the proof of the product rule is. Let’s recap one proof:

(fg)'(x) = \lim_{h \to 0} (f(x+h)g(x+h)-f(x)g(x))/h
= \lim_{h \to 0} (f(x+h)g(x+h)-f(x)g(x+h)+f(x)g(x+h)-f(x)g(x))/h
= \lim_{h \to 0} g(x+h)(f(x+h)-f(x))/h + f(x)(g(x+h)-g(x))/h
= g(x)f'(x)+f(x)g'(x).

It’s pretty awful. Maybe it isn’t that bad a proof as analysis goes but really, it’s unnecessary to subject normal people to such things: that can wait until a real analysis class.

The concept of limit is really difficult for a lot of people. So the solution (or one possible solution) is differentials. This is just replacing one vague concept (limits) with another that is even harder to formalise (differentials are really elements of the cotangent space to something, which is a bit scarier than epsilons and deltas).

But it’s historically accurate and as long as you are willing to accept a little bit of magic works quite well.

If y depends on x (basically is a function locally) then an ‘infinitesimal’ (really small but positive) change of x, called dx, leads to an infinitesimal change in y, called dy.

For example if y=x^2 then
y+dy=(x+dx)^2
x^2+dy=x^2+2xdx+(dx)^2
dy=2xdx

Notice (dx)^2=0. You can axiomatise this sort of behaviour (this is really dx \wedge dx = 0 or maybe this computation is in k[dx]/((dx)^2)) but this is expected behaviour for infinitesimals: they’re small enough that only linear terms matter.

The above calculation is ‘using the definition’. After you’ve done derivative rules you would just take d of both sides to go from
y=x^2
to
dy=2x dx

One property of the derivative is now that f(x+dx)=f(x)+f'(x)dx. This is (arguably) the real meaning of the derivative: it gives the best linear approximation of a function and infinitesimally this approximation is correct.

Now the proof of the product rule is much nicer:
if y = f(x)g(x)
y+dy=f(x+dx)g(x+dx)
dy = (f(x)+f'(x)dx)(g(x)+g'(x)dx)-f(x)g(x)
dy = f'(x)g(x)dx+f(x)g'(x)dx

This is a little more difficult to extend to integrals but who ever needs to use the definition of Riemann integral anyway? You can use whatever kind of approximations you want to find areas under curves: the only time you use the Riemann integral is when you have an antiderivative so can use the fundamental theorem of calculus.

The other big problem I have with calculus is that we pretend that functions are important when in science and geometry what you really care about are relations between things. We can do calculus on circles, and who knows whether distance is a function of velocity or the other way around….

Thoughts of a few other people on the matter:
Putting Differentials back. A very interesting paper on the issue with good references.

Calculus without Limits – Almost. A rather crazy textbook.

Other ways to teach calculus:
- These notes from Karl Heinz Dovermann define differentiability by a Lipschitz condition with exponent 2.
- Non standard analysis as seen in Keisler’s book
- Apparently there is a book that does everything with differential forms but I can’t find anything that is truly a single variable calculus text like this.

18 overs, none for 149

March 21, 2009 at 5:42 am | In Cricket | 4 Comments

There won’t be any specialist spin bowling in the Australian team for a while…

I don’t like it but the best bet for the Ashes is to play 4 quicks with North, Clarke and Katich to provide the spin bowling. The only question is if McDonald is worth picking as a bowler. If Clark is back I’d play him instead but I’m kind of warming to playing a medium pace bowler. He gets through overs at a decent pace, makes the batsman play, keeps the runs down. It’s pretty boring but I can see why medium pace bowlers used to be valuable.

Edited to Add: The other thought I have is wondering how bad Haddin’s keeping is? I didn’t watch last night but he gave up 19 byes in the innings. I don’t know enough about keeping to really judge it but people say Hartley is good. He averages only 28 with the bat in FC cricket but I think it’s feasible that he could save an extra 25 runs a game with the gloves (a catch plus 10 byes say) and that would make him basically as good. And with Johnson and McDonald he could bat at number 8 or 9.

Wooh! Spring Break!

March 13, 2009 at 8:30 am | In Life in America, Mathematics | 8 Comments

Things I plan to do:
- Go to some amount of Arizona Winter School on quadratic forms (I at least want to see John Conway and Noam Elkies talk) (That John Conway is certainly interesting…)
- Learn to program in C (well enough to do my homework anyway…)
- Use my newfound C programming skills to carry out simulation of CRC encoding/decoding, looking particularly at burst error detection capability (did you know that CRC-16 can detect about 99.9997% of length 16 burst errors?)
- Get Arizona ID of some form
- Get a haircut
- Watch world baseball classic (ongoing task)
- Do taxes ($120 refund federal, $50 refund state, inadvertent tax fraud a small possibility)
- Start researching projects for lattices class and algebraic geometry class
- clean some part of my house (bathroom)
- Write talk on coding theory for applied math colloquium (pretty much done)
- Get in some practice before start of softball season
- clean up backyard a bit

The decline of modern society

March 12, 2009 at 8:10 am | In Mathematics | 2 Comments

In January 2007 ISBNs changed from 10 digits to 13 digits. The new system has inferior error detection capabilities (there is no longer a guarantee that transposition of adjacent digits will be detected). Why was there not an outrage over this?

Australia v Cuba

March 10, 2009 at 7:12 pm | In Baseball | 16 Comments

- Travis Blackley starts for Australia. Strikes out the first batter.
- I don’t have tv coverage yet as the Dominican Republic v Netherlands game is in the 11th inning. Netherlands have the winning run at third base with one out!
- Blackley gives up a single and a double, gets a guy stealing and strikes one out to get out of the inning.
- The Netherlands hit a ball through the first baseman to win the game!!
- And we’ve got pictures. It’s 0-0 in the middle of the second.
- The Cuban starter Chapman is a lefty throwing 99mph. The defence looks good too: second base got to a ground ball up the centre, flipped it to the shortstop who threw the runner out at first. Collins hit one out to the warning track in right field and that was the inning.
- Cuba scores one run on a couple of hits plus a sac bunt but Blackley prevents any further damage: 1-0 in the middle of the third.
- Beresford hits a nice double the other way but Chapman dominates the rest of the Australian hitters and is up to 5 strikeouts in 3 innings. He’s thrown 40 pitches out of the maximum 70 though so he might not last more than a few more innings. 1-0 in the bottom of the third.
- Despite giving up a double and a balk(!) Blackley gets a groundout and strikeout to strand the runner at third. Still 1-0.
- Hughes doubles, a balk(!!) from Chapman and then after a few outs Risinger gets an RBI single! 1-1.
- Chapman gets a bit rattled with runners on base. Throws a wild pitch, Huber fouls off a few pitches. The game really slows down but the Cubans get the strikeout. 1-1 bottom of the fourth.
- Blackley has another good inning, only besmirched by a Beresford error at second base. 1-1 middle of the fifth.
- “accounts of this game may not be disseminated without the express written consent of the world baseball classic”. Well I’m breaking this rule.
- The new pitcher for Cuba throws a scoreless inning. Blackley hits the pitch limit and has to leave. 5 2/3 innings, 5 hits, 1 run. Great outing. In comes Damian Moss. Still 1-1.
- Moss gives up a homer to Cespedes! Gets the next out so it’s 2-1 to the bad guys in the middle of the 6th.
- A walk, a balk(!!!) and a sacrifice fly gets Hughes to 3rd base. Cuba brings in their closer Lazo. Pretty early move.
- Justin Huber singles to right field to bring in the runner. 2-2.
- Beresford up with the bases loaded and two outs! The Cubans are looking a little sloppy. And he gets a hit down the left field line. Two runners score! Lazo replaced! 4-2.
- Damian Moss gives up a two-out walk and a double that scores one. Then he gets the third out: 4-3. I don’t know too much about the Australia bullpen but I think we need some more runs….
- Cuba is really slowing this game down. A lot of visits to the mound. No one ever talks about the need to speed up baseball but this really is unnecessary.
- OH NO!! Rich Thompson was looking good with his curveball but some fat Cuban just hit a 2 run homer to take the lead. Score is 5-4 in the middle of the 8th.
- A few scoreless innings and we go to the bottom of the ninth. Here it is: 3 outs. Need a run or two.
- Oeltjen strikes out.
- Hughes grounds out to short. One more out.
- Snelling grounds out to second. Game over.

Australia plays Mexico tomorrow. Tough loss to bounce back from but who knows. I don’t know if I’ll be liveblogging but feel free to check out gameday on mlb.com

Australia v Mexico World Baseball Classic

March 8, 2009 at 9:37 pm | In Baseball | 2 Comments

- Game coming from Mexico city. It’s at 10000 ft elevation with short corner outfield fences so we should see some action.
- Australia scored 3 in the first inning with an Oeltjen single and home runs from Hughes and Snelling. The Mexican starter Oliver Perez (who is getting $12 million a year from the Mets) struggled.
- Craig Anderson got the start for Australia. As I predicted earlier he wasn’t fooling anyone, giving up 5 runs in the first inning.
- Anderson struggled further, leaving in the second after giving up 6 runs. But the relief crew of Mildren, Hendriks, Moss and Thompson were somewhere between good and lucky holding the Mexicans to 7 runs through 7 innings.
- Meanwhile the Australian bats kept talking and the Mexican pitching and fielding got sloppy. Oeltjen, Snelling, Harmon all had some good numbers.
- Currently it’s Australia 14, Mexico 7 in the top of the 8th. The Mexican body language is bad and Australia looks like moving on to play Cuba tomorrow Tuesday!
- Risinger hits a three run homer to take the score to 17 to 7. If we can hold the Mexican team scoreless in the bottom of the 8th then the game ends by the mercy rule.
- Rich Thompson pitching. Gets the ground out from Amezaga. Hairston strikes out looking against a nice curveball. Gives up a hit to Adrian Gonzalez – 2B Beresford can’t get the glove down quick enough on the artificial turf infield. Cantu strikes out swinging at the high heat.
- There it is. Early termination! Australia wins 17-7. Come back tomorrow Tuesday for Australia v Cuba.

Thoughts on the Australian Baseball Team

March 4, 2009 at 9:31 pm | In Baseball | Leave a Comment

- Who in Peoria is starting an “Aussie Aussie Aussie Oi Oi Oi” chant?
- I thought Australia was meant to be all pitching, no hitting. Well, they’re currently up 10-9 in the 6th inning against the Seattle Mariners.
- I like the look of Risinger, Huber and Roneberg with the bat. Of course it’s baseball so seeing someone hit 4 times tells you next to nothing about whether they are any good or not…
- The Australian fielding looks a bit dodgy – there were a couple of popups taken by the shortstop that I might have liked the outfielders to catch.
- The Australian uniform looks like the Oakland A’s.
- Craig Anderson doesn’t look like a very good pitcher. He just throws up these weird left hand floating things.
- Ryan Rowland-Smith (the turncoat who would rather earn money than pitch for Australia) was in the broadcast booth for a while. He at one point was about to explain the difference between rugby league and rugby union – one of my favourite topics of conversation – before the broadcasters cut him off.
- Adam Bright (the son of Ray Bright, really) faced one hitter in the 9th inning and gave up a double. Australia is defending an 11-9 lead. It would be more exciting if the Mariner’s cared about winning but still – Go Australia!
- Crawford gets the last three outs and that’s a win for Australia. Good warmup.

Talking

March 1, 2009 at 9:25 am | In Mathematics | 1 Comment

I gave a talk last week in the grad colloquium about why you can’t integrate e^(x^2) in terms of elementary functions. It went pretty well. Slides can be found here.

My philosophy in talks is definitely the less slides the better and the less actual mathematics the better. People just want to see amazing results, computer calculations, pretty pictures etc

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