Day 142
Well it finally happened, I forgot to write a blog yesterday. I easily could have, in fact there was a point where I sat down to do so but put it off for lack of any ideas. Then at 2am, half-asleep it just suddenly hit me that it never got done.
Oh well. Anyone who knows me should be shocked that I made it 140 consecutive days given my penchant for forgetting things and being generally disorganized.
But the writing shall continue! If I were to stop now on account of missing a day, that would mean the purpose of the blog was merely to say something, anything, daily. And that's only peripheral.
------------------------
Sometimes we make small-sounding propositions that actually carry with them other much larger propositions. Have you ever become completely comvinced you're just unluckier than other people at playing Risk, or that you get more green lights than average, or something similar? They sound like very plausible little propositions, mundane even.
But the truth is that they are stupendous, near-impossible claims to make. Say, for example, I hit 10 lights per day 250 days out of the year in a car. That's 2500 lights per year, with an average 50 percent chance of making green or red any given time. Say you drive for 5 years, and for some reason you're convinced that you get an inordinate number of green lights, say 6 out of 10.
I do wish I could do probability formulas but I don't have the mathematical know-how. But just from strait logic, I can say that the further a deviation from a 50/50 spread you have (given an even probility on each light), the less likely it becomes, because there are proportionally fewer possible combinations that will produce that result.
Think coin tosses (same thing, different objects). You have better odds of tossing HT or TH in two throws than tossing TT or HH. The reason is that there are 2 ways in which you can get a head and a tail (order being irrelevant here) and only one way each to get HH or TT. Likewise, let's look at the possible combinations for, say 3 coin tosses:
TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
Again, with the order of the tosses being irrelevent, you only have a 1/8 chance of tossing all tails, while you have a 3/8 chance of tossing two tails and a heads, and a 3/8 chance of tossing two heads and a tails. So even with just three coins, you're at a 75% probability that they won't all match.
Use your intuition here. The larger the number gets, the more packed the proportional deviation from the mean will become, and the more likely you are to end up proportionally closer to the mean. Flip a hundred coins, and it is very likely you'll be near 50 of each heads and tails. Flip a million coins, and you'll invariably be extremely close to 50% of each heads and tails.
So in your 5 years of driving you've encountered over 12,000 lights. The odds that your average ranges any outside of, say, even 2 percent (240 lights in either direction) of 6000 red and 6000 green are staggeringly low, and two percent you'd never even notice anyway. Push that number to ten percent, i.e. 7200 green and 4800 red, (you may notice that over time) and the odds far surpass even the most unlikely of lottery tickets by many, many zeros.
To the world of people who genuinely believe that luck or bad luck favours them as a rule I offer the following: consider the possibility that you formed the belief after having an odd stint of luck in one direction (perfectly normal on occasion), and then you semi-consciously learned to notice and record every instance of your belief being validated and tended to forget the instances in which it was disconfirmed. It is much easier, and more likely, that we manage to convince ourselves of certain truths because we are looking to remember evidence of confirmation and forget the rest, than it is that the laws of probability are suspended just for a select few people.
Oh well. Anyone who knows me should be shocked that I made it 140 consecutive days given my penchant for forgetting things and being generally disorganized.
But the writing shall continue! If I were to stop now on account of missing a day, that would mean the purpose of the blog was merely to say something, anything, daily. And that's only peripheral.
------------------------
Sometimes we make small-sounding propositions that actually carry with them other much larger propositions. Have you ever become completely comvinced you're just unluckier than other people at playing Risk, or that you get more green lights than average, or something similar? They sound like very plausible little propositions, mundane even.
But the truth is that they are stupendous, near-impossible claims to make. Say, for example, I hit 10 lights per day 250 days out of the year in a car. That's 2500 lights per year, with an average 50 percent chance of making green or red any given time. Say you drive for 5 years, and for some reason you're convinced that you get an inordinate number of green lights, say 6 out of 10.
I do wish I could do probability formulas but I don't have the mathematical know-how. But just from strait logic, I can say that the further a deviation from a 50/50 spread you have (given an even probility on each light), the less likely it becomes, because there are proportionally fewer possible combinations that will produce that result.
Think coin tosses (same thing, different objects). You have better odds of tossing HT or TH in two throws than tossing TT or HH. The reason is that there are 2 ways in which you can get a head and a tail (order being irrelevant here) and only one way each to get HH or TT. Likewise, let's look at the possible combinations for, say 3 coin tosses:
TTT, TTH, THT, THH, HTT, HTH, HHT, HHH
Again, with the order of the tosses being irrelevent, you only have a 1/8 chance of tossing all tails, while you have a 3/8 chance of tossing two tails and a heads, and a 3/8 chance of tossing two heads and a tails. So even with just three coins, you're at a 75% probability that they won't all match.
Use your intuition here. The larger the number gets, the more packed the proportional deviation from the mean will become, and the more likely you are to end up proportionally closer to the mean. Flip a hundred coins, and it is very likely you'll be near 50 of each heads and tails. Flip a million coins, and you'll invariably be extremely close to 50% of each heads and tails.
So in your 5 years of driving you've encountered over 12,000 lights. The odds that your average ranges any outside of, say, even 2 percent (240 lights in either direction) of 6000 red and 6000 green are staggeringly low, and two percent you'd never even notice anyway. Push that number to ten percent, i.e. 7200 green and 4800 red, (you may notice that over time) and the odds far surpass even the most unlikely of lottery tickets by many, many zeros.
To the world of people who genuinely believe that luck or bad luck favours them as a rule I offer the following: consider the possibility that you formed the belief after having an odd stint of luck in one direction (perfectly normal on occasion), and then you semi-consciously learned to notice and record every instance of your belief being validated and tended to forget the instances in which it was disconfirmed. It is much easier, and more likely, that we manage to convince ourselves of certain truths because we are looking to remember evidence of confirmation and forget the rest, than it is that the laws of probability are suspended just for a select few people.
Comments