Month: November 2024

my knee self diagnosis: patellafemoral syndrome (runners knee)

alan Leave a comment

since increasing my weekly milelage from 10 to 16 i started noticing mild pain on the medial sides of both of my knee caps (my right more so than my left). i also added superfeet arch insoles into my shoes at around the same time, so that may have also affected my running mechanics.

from what i’ve been able to research, the most likely culprit is patellafemoral syndrome aka runners knee given the proximity of the pain to the knee cap. it’s on the medial side just underneath the knee cap. this hasn’t really seriously affected my daily mobility or even my running since it’s very mild, but it’s something i want to make sure i nip in the bud before it develops

here’s a table of common causes and which ones i believe apply to me

causeapplies?
kneecap misalignmentdon’t know
overuse most likely. 10 -> 16 is a 60% increase! recommended is closer to 10 – 15%
injury or traumano
week thigh musclespossible – i haven’t incorporated quad strengthening into my routine yet
tight hamstringsunlikely, esp. because i stretch these during yoga often
tight achilles tendonsmaybe, i don’t stretch my achilles
poor foot supportcould be affected by my new arch “supports” that may be throwing off my normal gait
feet rolling inmaybe? most of the roads and sidewalks i run on have camber/slope. when i run on the road, i run on the left so there’s a leftward slope which i’m sure affects my foot roll motion

of this set of causes, the top ones are likely

my current recovery plan is

  • incorporate quad strengthening exercises with focus on compound movements
    • sumo squats
    • bulgarian split squats
    • squat jumps
    • lateral jumps
  • stretch calfs and achilles post-run
  • reduce weekly miles from 16 to 14 or even back to 10-12 per week
    • shift my current 8,2,3,3 pattern to 4,1,2,3 (halving my long run, then progressive increase throughout week)
  • remove the arch supports from my shoe (it’s an extra variable i don’t want to keep around…)
  • icing knees at end of day to reduce inflammation
  • knee cap mobilization exercises, also EOD

i’ll do another report in 3 weeks and let you know how it went!

xor and mod 2

alan Leave a comment

so there’s a interesting property between the XOR operation and mod 2

turns out, the xor (^) of any sequence of bits is equal to the sum of those bits modulo 2

for example

1 ^ 0 ^ 1 ^ 1 is the same as (1 + 0 + 1 + 1) % 2

if you take this step by step, the xor side:

1 ^ 0 = 1

1 ^ 0 = 1

1 ^ 1 = 0

0 ^ 1 = 1 (answer)

the modulo side:

1 + 0 + 1 + 1 = 3

3 % 2 = 1

why?

lets look at the truth table for XORs using two bits

left bitright bitxor result
000
011
101
110
xor table

XOR is an exclusive OR, so it will only be 1 if there’s ONLY ONE bit that’s on. if there’s two bits or no bits, the result is 0. what other operation of two operands where the result is 0 given 0 and 0 and 1 and 1? modulo 2!

this equivalence exists because when we’re dealing with two bits, their sum is 2. 2 mod 2 is 0. when both bits are 0, the sum is 0 and 0 mod 2 is 0. when only one of them (and odd number) is on, we always get a sum of 1 and 1 mod 2 is 1

even though we’re only looking at two bits, this actually generalizes to any sequence of bits because it turns out that XORing any sequence of bits results in 0 when there is an even number of 1 bits and 1 when there is an odd number of 1 bits (or none)

short vs middle vs long distance

alan Leave a comment

ever wondered what it means for a runner to be a “middle distance” or “long distance” runner? in the running / racing world there’s three main categories of distance events that differ by distance ranges

short or sprint distance

these are traditional 100 meter (100m), 200m, 400m, and the 4x100m and 4x400m relays. these are pretty much purely anaerobic events. anything beyond 400m is in the middle distance category where the running starts to demand both high aerobic and anaerobic work

medium distance

common track distances are the 800m, 1500m, milers (1609m) , 3000m and the steeple chase variations involving obstacles and water jumps. anything beyond 3000m is going to be long distance

long distance

this is where my current comfort level is with running, although i do most of my higher intensity work in the short distances. common races in this range are the 5000m or 5k (though some people also consider the 5k a medium distance event), 10k, half marathon (21k), marathon (42k), and beyond (ultra marathons) like a 50k (31 miles). pretty much most road racing and cross country running fall into long distance category.

the longest official race i’ve run so far is a super popular local 15k (https://www.boilermaker.com/). i’ve been running this race in the last 3 years. my impression is that the 15k is not a common race distance (compared to the 10k) because when i share this with people they always express surprise that such a distance is even a thing. my goal next year is to run a half marathon, so hopefully that will be my new long race record!

boilermaker fun fact: the boilermaker actually draws a good number of elite international runners – this past year the winner was john korir of kenya who’s one of the current top 10 marathon record holders!

boilermaker fun fact 2: not sure if this is verified, by i learned this through my wife. the event takes place in july, which seems odd because it’s a distance event that’s smack in the height of summer heat. but this is a couple of months before the marathon majors in the U.S (nyc, boston, chicago…) that run between september – november, so this off season schedule suits international runners that are training for the majors.

anyway, here’s an easy / quick way to remember these ranges

short distance – up to a single lap on a standard outdoor track (400m)

medium distance – up to a 3k / two miles / 8 laps on a standard outdoor track

long distance – everything else