Achilles tendons still hurting... it's been 8 days now. I plan to swim today, that's it. Though I'm almost done putting together a strength-training regimen to start soon.
This morning on the way to camp, Jesse asked me what's bigger, a googol factorial or a googolplex. I told him I wasn't sure without paper, but he wanted me to guess.
Then I recalled that using a simple integral lowerbound, we know that (n/e)ne ≤ n!. (You get this from taking ln of n!, converting to a sum; then integrate ln x to get x ln x - x, and evaluate over [1,n] to get n ln n - n + 1. Taking e to this power gives the lowerbound (n/e)ne ≤ n!)
This makes it easy. Let g be a googol. Recall a googol is 10100 and a
googolplex is 10g. Then g! > (g/e)g e > (g/10)g = 1099g > 10g. So g! is definitely bigger than a googolplex. By a lot, in fact.
Tuesday, June 22, 2010
Monday, June 21, 2010
Adventures of an Invalid
Pronouncing "invalid" as a noun is all the rage among my family this week: daddy hasn't walked very well. But today was Father's Day, and I was motivated to be more valid than in the past 5 days.
Sandra took the boys around 10:30pm up to Longmont, leaving me the day to do whatever I wanted. After cleaning the house for a while, I headed to Lakeshore to swim about 1000 yds. Then back home, Sandra called and said they were going to have dinner in Longmont and I was invited.
Instead of driving up, I decided to bike (about 25 miles from Superior). This, in spite of my still-painful Achilles tendinopathy.
Around 2:15pm, under fairly dark skies, I headed out Rock Creek Parkway, turning right on 88th St, then left on Dillon. To avoid straining my Achilles tendons, I was pedaling with my heels over the clipless pedals (instead of the balls of my feet, which is more natural and which would be mandatory if I wore cleats). Also, I pointed my toes downward to keep my Achilles compressed rather than extended. This seemed to work well.
I'd resolved not to push myself too hard: although I was aerobically in good enough shape to hold 80% HR for 2 hours, my body was not at all used to cycling and I really didn't want another injury to compound the current one. So I stopped periodically to massage my legs, stretch, drink, etc.
Up McCaslin to South Boulder, then the long downhill into Boulder. Right on Cherryvale, left on Baseline, right on 55th, left on Pennsylvania, over Foothills on the overpass, then up to 30th and Arapahoe for a Jamba Juice.
Although it would have been shorter to just take 96th straight north to Longmont, I was taking the scenic route for 2 reasons: (1) food and drink along the way, and (2) I could always puss out and take the bus if I started feeling joint pain or whatever.
The diagonal was monotonous an quite trafficked, as usual. Arrived in Longmont around 4:40pm only to find Sandra had left! Now I would need to ride back home as well?
Fortunately, she was only in Boulder playing mini-golf with the kids, so she came back up to have dinner (which had previously been aborted), then we drove home this evening.
Still massaging my calves with The Stick (tm) and icing my Achilles. Feel fine, and hoping for the best tomorrow. (I never get to know if I'm injured or not until the next day, it seems.)
All in all, a good Father's Day.
Sandra took the boys around 10:30pm up to Longmont, leaving me the day to do whatever I wanted. After cleaning the house for a while, I headed to Lakeshore to swim about 1000 yds. Then back home, Sandra called and said they were going to have dinner in Longmont and I was invited.
Instead of driving up, I decided to bike (about 25 miles from Superior). This, in spite of my still-painful Achilles tendinopathy.
Around 2:15pm, under fairly dark skies, I headed out Rock Creek Parkway, turning right on 88th St, then left on Dillon. To avoid straining my Achilles tendons, I was pedaling with my heels over the clipless pedals (instead of the balls of my feet, which is more natural and which would be mandatory if I wore cleats). Also, I pointed my toes downward to keep my Achilles compressed rather than extended. This seemed to work well.
I'd resolved not to push myself too hard: although I was aerobically in good enough shape to hold 80% HR for 2 hours, my body was not at all used to cycling and I really didn't want another injury to compound the current one. So I stopped periodically to massage my legs, stretch, drink, etc.
Up McCaslin to South Boulder, then the long downhill into Boulder. Right on Cherryvale, left on Baseline, right on 55th, left on Pennsylvania, over Foothills on the overpass, then up to 30th and Arapahoe for a Jamba Juice.
Although it would have been shorter to just take 96th straight north to Longmont, I was taking the scenic route for 2 reasons: (1) food and drink along the way, and (2) I could always puss out and take the bus if I started feeling joint pain or whatever.
The diagonal was monotonous an quite trafficked, as usual. Arrived in Longmont around 4:40pm only to find Sandra had left! Now I would need to ride back home as well?
Fortunately, she was only in Boulder playing mini-golf with the kids, so she came back up to have dinner (which had previously been aborted), then we drove home this evening.
Still massaging my calves with The Stick (tm) and icing my Achilles. Feel fine, and hoping for the best tomorrow. (I never get to know if I'm injured or not until the next day, it seems.)
All in all, a good Father's Day.
Saturday, June 19, 2010
Mt Washington
Looks like Denver Marathon Winner Chris Siemers won the Mt Washington Road Race today. And Green Mtn FKT holder Rickey Gates came in 4th.
This is probably the most prestigious uphill road race in the country. Gratz to all who competed!
This is probably the most prestigious uphill road race in the country. Gratz to all who competed!
Mt Evans Spectating?? .... nah
I woke up at 4am today thinking I might drive down to Mt Evans and watch the ascent race. I could probably help a few ppl down from the top as well (people often need rides down).
It was probably best that I decided to just sleep in. I don't seem to sleep well anymore this past year, and I wake up a lot through the night.
No results on Evans yet; I hope Jeff Valliere does well. I like his blog.
I've been swimming lately, since I can't run now. Heels are still painful, and it's been almost a week since I last did a hill. Patience I guess... :)
It was probably best that I decided to just sleep in. I don't seem to sleep well anymore this past year, and I wake up a lot through the night.
No results on Evans yet; I hope Jeff Valliere does well. I like his blog.
I've been swimming lately, since I can't run now. Heels are still painful, and it's been almost a week since I last did a hill. Patience I guess... :)
Thursday, June 17, 2010
So frustrating
Swimming, Jacuzzi, stretching, calf massage, ice. All trying to keep my feet healthy.
Today at work, my feet hurt. Plantar pain (probably from trying that running orthotic, which doesn't have much arch support compared to my walking orthotic). And worst of all, achilles pain.
I mean... what? All I did was walk slowly on a flat trail with padded shoes.
Playing kickball tonight with a neighborhood team in the Superior league. I can't run. This will be fun. :(
Supposed to hike Green Mtn tomorrow with Andy. Might have to postpone. Sigh...
Today at work, my feet hurt. Plantar pain (probably from trying that running orthotic, which doesn't have much arch support compared to my walking orthotic). And worst of all, achilles pain.
I mean... what? All I did was walk slowly on a flat trail with padded shoes.
Playing kickball tonight with a neighborhood team in the Superior league. I can't run. This will be fun. :(
Supposed to hike Green Mtn tomorrow with Andy. Might have to postpone. Sigh...
Wednesday, June 16, 2010
Achilles Tendonosis
Went to the doc this morning. He says no running for 2 weeks and lay off the hills.
Sigh... not sure how to train for Long's Peak without doing hills.
Sigh... not sure how to train for Long's Peak without doing hills.
Doudy Draw loop
Slow walk today with Andy. Flatirons vista, Doudy Draw, Community Ditch, cross 93, Greenbelt Plateau, back to car. 2:18 slow hiking. I used poles for the first time ever, just to keep some weight off my injured feet. I also used Asics trail runners (GS 2150s) with a running orthotic.
Felt fine. No aches, no pain.
Got back home, ate some dinner around 7pm, then off to the pool. Did 7x100 on the 3mins, lifted some weights, sat in the jacuzzi letting my feet get massaged a bit. Then went home and iced.
I wore this ridiculous Strassburg Sock to bed. It's supposed to help Achilles and Plantar problems, but mostly it just made it hard to sleep. I wore it on my right foot only, and in the morning I really couldn't tell any difference.
Felt fine. No aches, no pain.
Got back home, ate some dinner around 7pm, then off to the pool. Did 7x100 on the 3mins, lifted some weights, sat in the jacuzzi letting my feet get massaged a bit. Then went home and iced.
I wore this ridiculous Strassburg Sock to bed. It's supposed to help Achilles and Plantar problems, but mostly it just made it hard to sleep. I wore it on my right foot only, and in the morning I really couldn't tell any difference.
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