Warning: This entry contains no math.
It seems that I touched on something so much larger than I had given much thought to when I wrote that last blog about what I called the elasticity of time. I was talking about just one aspect of how humans perceive time and one particular phenomenon that may be useful to consider when gauging the long term perception of the passage of time (ie. when are you really halfway through your career?). But when you start talking about time and how we perceive it, man it gets really interesting really fast.
Years ago I read what remains one of my favorite nonfiction books, Phantoms in the Brain, by Dr. V.S. Ramachandran and Sandra Blakeslee (with a forward by neurologist superstar Oliver Sacks). The book sets about explaining the various things that we have learned about the brain and specific regions in it as a result of tiny malfunctions in those regions. One area that I found particularly interesting had to do with vision and all of the things that can go wrong with our eyesight. There are literally dozens of different pathways and channels having to do with what we think of as vision and each one controls a different aspect. Some parts are concerned with motion and if they don't work properly you may experience the world in a strobe like pattern instead of fluid. Some parts are responsible for attaching emotion to what we see, others are responsible for recognizing faces. Some parts are responsible for processing colors while others are responsible for processing shades. It's possible to go blind in only one hemisphere, meaning that both of your eyes can only see to the right, or to the left. It's even possible to be consciously blind while subconsciously sighted. The point that I'm trying to make is that we may sometimes think of vision as one sense, as one thing. But the reality is that it's so complex and there are so many things that we "see." It's hard to imagine what a miracle is happening in all of our brains when we are sighted, how many different systems are working together to create an image that makes sense to us.
The perception of time is very much like this. There are so many processes involved in understanding what time means to us. One friend pointed me in the direction of the telescoping effect, which is the feeling that things that occurred long ago did not occur as long ago, and that things that happened relatively recently can feel like they happened much further in the past. There are also numerous interesting studies (like this one) on the effect of deprivation on our circadian rhythm.
It turns out that it doesn't take much to drastically alter our short term perception of time passing. This does beg the question on what being permanently blind does to a person's natural rhythm. I imagine that over time their brains figure it out and adjust accordingly, using other methods of tracking the passage of time (such as clocks).
Then there is the oddball effect, the feeling that time slows down for certain dramatic or dangerous events. I still remember a car accident I had more than 18 years ago that seemed to happen entirely in bullet time. Again, I fall back to radiolab to brilliantly explain this phenomenon and one particular experiment designed to describe it.
Anyway, the point of all of this is that time is crazy. Our perception of time is crazier. I only meant to address the tiniest facet of it originally, but I thank everyone for making me take a much bigger look at it. Science is pretty cool.
Friday, February 7, 2014
Tuesday, February 4, 2014
The Elasticity of Time
Sorry about the delay since my last entry. I had a couple of things I wanted to say about cars that just really got away from me. I've decided to move on (and maybe finish them later).
What I've been thinking about today is a concept that I like to call the elasticity of time. I'm sure there is some other term for the phenomenon, but I am too lazy to look it up.
I'm referring to a concept that I am sure everyone has experienced: the feeling that time seems to pass faster and faster as we get older. If this phenomenon is not universal, then it must at least be widespread, for I've never encountered anyone who didn't know what I was talking about when I brought it up.
Here are my questions:
1. Is the elasticity of time universal?
2. If it is, is it experienced in a universal fashion?
3. If it is experienced in a universal fashion, what is the nature of that fashion?
4. How can this information be used to make our lives a little better?
1. I believe it is universal. If it is not, then it seems at the very least to be universal within our culture, which can still be highly relevant. I suppose the only way to know for certain would be to study people of vastly different cultures and see if they experience a similar acceleration in the perception of time passing.
2. What I mean by this is whether or not everyone experiences the phenomenon in roughly the same way. Does the difference of one year at 30 relative to one year at 20 feel about the same for you as it does for me? I realize that this is a fairly subjective thing, as we are talking about how long a period of time feels. But I would argue that you can still make a fairly objective assessment about how long time feels to large groups of people.
3. This is just a guess, but right now it's as good as any. I would hypothesize that the perception of the speed of a period of time is relative to the amount of memory that a person has over their lifetime. Meaning that the reason a year feels shorter when you are 20 than it did when you were 10 is because when you were 10, it represented 10% of your total lifespan, versus only 5% when you are 20.
4. How can this be used? This is where it gets interesting. Let's first take a look at life expectancy in the United States, it's 78.6 years. We'll call it 79. Now let's take a look at how long a year feels. Normally, I would discount the first few years of childhood as nobody has a working memory of being an infant and this whole thing is kind of dependent upon the memory of time, but for simplicity's sake, I'm just going to leave it in. From 0-1 a year is 100% of your life, from 1-2, 50%, from 2-3, 33%, and so on. like this
First year - 100%
Second year - 50%
...
Seventy Ninth year - 1.27%
Total - 495.3%
Well, this can't be right.
Using only that most simple of formulas speculating that each year feels differently relative to how much of your lifespan it represents means that an average lifespan would only subjectively feel like five times the length of the first year. Put another way, at 30 years old it means that one year should feel like only 0.67% of an entire life (3.33% / 495.3%). This would suggest that an actual lifespan would feel like 148 years to a 30 year old. Somehow, I doubt this to be correct.
Then what is the formula?
Maybe it's not that we're on the wrong track here. Maybe it's just that we're starting too early. As I said before, nobody remembers their first years. Even once memories do start to form, there's still a ton of development and craziness happening that makes all of that time a little tricky to factor in with all of the rest of the time I spend, you know, being human.
What happens if I start the clock when I first noticed how much quicker one year felt from the last. For me, it was probably right around adolescence. I'll start at 13. Like this
13th year - 7.69%
14th year - 7.14%
...
Seventy Ninth year - 1.27%
Total - 184.98%
Suddenly this looks a lot closer to how it actually feels. This means that a year to a 13 year old is over 4% of their subjective life expectancy (which helps explain why people over 30 seem so ancient to teenagers). This also means that a year at 30 is going to feel 50% faster than a year at age 20 and a year at age 40 is going to feel a full third faster than a year at 30. This isn't actually too unreasonable.
What actually got me thinking about all of this is how much I hate working. Say you graduate from college at 21 and enter into the workforce. Also say that you somehow manage to get one of these great careers that you will actually be able to retire from at 60. Now say that you're, I don't know, 34, and you just want to know subjectively how much time you have left. Now we have a formula for that:
x = (1/21 + 1/22 + 1/23.....1/n) divided by (1/21 + 1/22 + .... 1/60) wherein n is your age.
What I get is 48.09%. What this means is that even though I have only worked for one third of my estimated working life, it should feel like I am very nearly half way done given the subjective acceleration of time. In another year I will be full on half-way through the muck. Yippee.
What I've been thinking about today is a concept that I like to call the elasticity of time. I'm sure there is some other term for the phenomenon, but I am too lazy to look it up.
I'm referring to a concept that I am sure everyone has experienced: the feeling that time seems to pass faster and faster as we get older. If this phenomenon is not universal, then it must at least be widespread, for I've never encountered anyone who didn't know what I was talking about when I brought it up.
Here are my questions:
1. Is the elasticity of time universal?
2. If it is, is it experienced in a universal fashion?
3. If it is experienced in a universal fashion, what is the nature of that fashion?
4. How can this information be used to make our lives a little better?
1. I believe it is universal. If it is not, then it seems at the very least to be universal within our culture, which can still be highly relevant. I suppose the only way to know for certain would be to study people of vastly different cultures and see if they experience a similar acceleration in the perception of time passing.
2. What I mean by this is whether or not everyone experiences the phenomenon in roughly the same way. Does the difference of one year at 30 relative to one year at 20 feel about the same for you as it does for me? I realize that this is a fairly subjective thing, as we are talking about how long a period of time feels. But I would argue that you can still make a fairly objective assessment about how long time feels to large groups of people.
3. This is just a guess, but right now it's as good as any. I would hypothesize that the perception of the speed of a period of time is relative to the amount of memory that a person has over their lifetime. Meaning that the reason a year feels shorter when you are 20 than it did when you were 10 is because when you were 10, it represented 10% of your total lifespan, versus only 5% when you are 20.
4. How can this be used? This is where it gets interesting. Let's first take a look at life expectancy in the United States, it's 78.6 years. We'll call it 79. Now let's take a look at how long a year feels. Normally, I would discount the first few years of childhood as nobody has a working memory of being an infant and this whole thing is kind of dependent upon the memory of time, but for simplicity's sake, I'm just going to leave it in. From 0-1 a year is 100% of your life, from 1-2, 50%, from 2-3, 33%, and so on. like this
First year - 100%
Second year - 50%
...
Seventy Ninth year - 1.27%
Total - 495.3%
Well, this can't be right.
Using only that most simple of formulas speculating that each year feels differently relative to how much of your lifespan it represents means that an average lifespan would only subjectively feel like five times the length of the first year. Put another way, at 30 years old it means that one year should feel like only 0.67% of an entire life (3.33% / 495.3%). This would suggest that an actual lifespan would feel like 148 years to a 30 year old. Somehow, I doubt this to be correct.
Then what is the formula?
Maybe it's not that we're on the wrong track here. Maybe it's just that we're starting too early. As I said before, nobody remembers their first years. Even once memories do start to form, there's still a ton of development and craziness happening that makes all of that time a little tricky to factor in with all of the rest of the time I spend, you know, being human.
What happens if I start the clock when I first noticed how much quicker one year felt from the last. For me, it was probably right around adolescence. I'll start at 13. Like this
13th year - 7.69%
14th year - 7.14%
...
Seventy Ninth year - 1.27%
Total - 184.98%
Suddenly this looks a lot closer to how it actually feels. This means that a year to a 13 year old is over 4% of their subjective life expectancy (which helps explain why people over 30 seem so ancient to teenagers). This also means that a year at 30 is going to feel 50% faster than a year at age 20 and a year at age 40 is going to feel a full third faster than a year at 30. This isn't actually too unreasonable.
What actually got me thinking about all of this is how much I hate working. Say you graduate from college at 21 and enter into the workforce. Also say that you somehow manage to get one of these great careers that you will actually be able to retire from at 60. Now say that you're, I don't know, 34, and you just want to know subjectively how much time you have left. Now we have a formula for that:
x = (1/21 + 1/22 + 1/23.....1/n) divided by (1/21 + 1/22 + .... 1/60) wherein n is your age.
What I get is 48.09%. What this means is that even though I have only worked for one third of my estimated working life, it should feel like I am very nearly half way done given the subjective acceleration of time. In another year I will be full on half-way through the muck. Yippee.
Monday, December 30, 2013
Lotteries
I tend to think about the lotto probably more than I should, especially for someone who very rarely or almost never plays it. I'm often fascinated by things we do as a human mob, as the aggregate. Often enough, through sheer randomness, a mass of people begins to organize and group and do really smart things without even meaning to. There's a radiolab episode about emergence which discusses this very thing. But sometimes, plenty of times, really, we do exactly the opposite. We do really dumb things. The lottery is one of those times (health insurance is another*).
In the lottery, a very large group of people get together and each of them buys a ticket with the same face value in the chances that one of them will win a very large sum. Here's the problem: that very large sum never equals the total amount that was collected for tickets. In the aggregate it's like having a person say "I want to spend a billion dollars so that I can win $350 million." Only a fool would do this. But break this process into the mob and we are millions of fools, who do this over and over and over again, and have practically since the beginning of time.
Let's talk about the value of a ticket for a second. Let's pretend that nobody else is taking a cut. There is no lottery commission taking a fee to run the game, and there are no taxes to be paid on winnings. Let's also pretend that every ticket costs exactly one dollar and has exactly the same chance of winning. In this case, in this perfect game, the actual expected value of each ticket really is $1. Let's say it's the mega millions game, where your chances of winning the jackpot are 1 in 258,890,850. For simplicity's sake, I'm going to forget about all of the minor prizes and how they affect overall odds as well as multiple winners and how they affect the jackpot. That $1 has a 0.00000038626316843566% chance of winning the jackpot. If the jackpot were say, only $100 million, then you could say that the value of the ticket was 0.0000000038626316843566 * $100,000,000 or roughly 39 cents. In order for the expected value of the ticket to rise to the full $1, the jackpot has to rise to $258,890,850.
The way that lotteries actually run is that the ticket is never worth the full $1. Not even close. In fact, it's usually closer to the 39 cents, meaning that every time we buy a ticket, we are instantly throwing away nearly two thirds of our money (or, in my experience, all of it). So why do we do this? It comes down to utility.
If you are completely new to economics utility is essentially the value that we perceive an item to have based on its usefulness to us. The more of the item we have, typically the less utility each one has. Imagine the value of a banana if you were starving to death. It has a lot of utility.
Now imagine that you are a billionaire. I have for sale two lottery tickets. Each one costs $10,000. One ticket, the billion dollar lottery, has a 1% chance of winning $1,000,000,000. The other ticket, the one hundred thousand dollar ticket, has a 99% chance of winning $100,000. Which one would you buy? I think most billionaires who could afford the $10,000, and who might scoff at $100,000 would look at the expected value of each ticket. The expected value of the billion dollar ticket is one percent of one billion, or $10 million. The expected value of the hundred thousand dollar ticket, likewise, is 99% of $100,000, or $99,000. In either case, the ticket is a smart bet, but the billion dollar ticket is way smarter. But try to remember you have a 99% chance of losing ten grand.
Now imagine that you're you. You don't have $10,000 to lose. Which one do you buy? Do you even skip out altogether and not even play, choosing not to risk it on the 1% chance that you lose everything? This is the difference that utility makes.
People play the lottery because it gives them something that they value. It gives them hope, a thrill that they just might overcome the staggering odds and win huge. It just blows my mind that this utility is worth 2/3 of their money. It blows my mind that so many people do it.
I tend to believe that around 90% of the time that money changes hands between two parties, one of those parties is getting ripped off. The only time they aren't is when the value equals the price, which is rare. If you're not sure which party is getting ripped off, it's almost certainly you. Why we do it en masse is beyond me.
*I say this about health insurance because on the aggregate level the insurance industry really just exists to pay the bill. Imagine if the total number of patients were collectively pooled into Group A. Next, the insurance industry can be pooled into Group B. Finally, the medical community is thrown together in Group C. What we do in this country is akin to saying "Group A owes Group C $10. Let's pay Group B $15 to pay Group C." It boggles my mind.
In the lottery, a very large group of people get together and each of them buys a ticket with the same face value in the chances that one of them will win a very large sum. Here's the problem: that very large sum never equals the total amount that was collected for tickets. In the aggregate it's like having a person say "I want to spend a billion dollars so that I can win $350 million." Only a fool would do this. But break this process into the mob and we are millions of fools, who do this over and over and over again, and have practically since the beginning of time.
Let's talk about the value of a ticket for a second. Let's pretend that nobody else is taking a cut. There is no lottery commission taking a fee to run the game, and there are no taxes to be paid on winnings. Let's also pretend that every ticket costs exactly one dollar and has exactly the same chance of winning. In this case, in this perfect game, the actual expected value of each ticket really is $1. Let's say it's the mega millions game, where your chances of winning the jackpot are 1 in 258,890,850. For simplicity's sake, I'm going to forget about all of the minor prizes and how they affect overall odds as well as multiple winners and how they affect the jackpot. That $1 has a 0.00000038626316843566% chance of winning the jackpot. If the jackpot were say, only $100 million, then you could say that the value of the ticket was 0.0000000038626316843566 * $100,000,000 or roughly 39 cents. In order for the expected value of the ticket to rise to the full $1, the jackpot has to rise to $258,890,850.
The way that lotteries actually run is that the ticket is never worth the full $1. Not even close. In fact, it's usually closer to the 39 cents, meaning that every time we buy a ticket, we are instantly throwing away nearly two thirds of our money (or, in my experience, all of it). So why do we do this? It comes down to utility.
If you are completely new to economics utility is essentially the value that we perceive an item to have based on its usefulness to us. The more of the item we have, typically the less utility each one has. Imagine the value of a banana if you were starving to death. It has a lot of utility.
Now imagine that you are a billionaire. I have for sale two lottery tickets. Each one costs $10,000. One ticket, the billion dollar lottery, has a 1% chance of winning $1,000,000,000. The other ticket, the one hundred thousand dollar ticket, has a 99% chance of winning $100,000. Which one would you buy? I think most billionaires who could afford the $10,000, and who might scoff at $100,000 would look at the expected value of each ticket. The expected value of the billion dollar ticket is one percent of one billion, or $10 million. The expected value of the hundred thousand dollar ticket, likewise, is 99% of $100,000, or $99,000. In either case, the ticket is a smart bet, but the billion dollar ticket is way smarter. But try to remember you have a 99% chance of losing ten grand.
Now imagine that you're you. You don't have $10,000 to lose. Which one do you buy? Do you even skip out altogether and not even play, choosing not to risk it on the 1% chance that you lose everything? This is the difference that utility makes.
People play the lottery because it gives them something that they value. It gives them hope, a thrill that they just might overcome the staggering odds and win huge. It just blows my mind that this utility is worth 2/3 of their money. It blows my mind that so many people do it.
I tend to believe that around 90% of the time that money changes hands between two parties, one of those parties is getting ripped off. The only time they aren't is when the value equals the price, which is rare. If you're not sure which party is getting ripped off, it's almost certainly you. Why we do it en masse is beyond me.
*I say this about health insurance because on the aggregate level the insurance industry really just exists to pay the bill. Imagine if the total number of patients were collectively pooled into Group A. Next, the insurance industry can be pooled into Group B. Finally, the medical community is thrown together in Group C. What we do in this country is akin to saying "Group A owes Group C $10. Let's pay Group B $15 to pay Group C." It boggles my mind.
Friday, December 27, 2013
Billions and billions
7.13 Billion. That is the current number of human inhabitants on the earth. It's a staggering number and a little hard to get your head around. Each person, every one of you, is 0.000000014% of the total population. Isn't that nuts? There are so many people that if you were to spend just one second at a time in the lives of each and every one of us, it would take 226 years. According to Wolfram Alpha, the average age on earth is 27.6 years. What this means is that on earth, right now, there is 196.8 billion years of human life experience. This is fourteen times the accepted age of the universe, which is only 13.8 billion. Let that sink in.
In the United States, the population is 319 million. The GDP of the United States is 16.91 trillion. This means that, per person, the total average value produced per year in this country is $53,009. This only gets crazier when you realize that this number is counting all residents, not just those working. According to the U.S. Bureau of Labor and Statistics, the labor force in the United States is right around 155 million. This means that each laborer in this country contributes an average of $109,000 to our economy. Now, there are two things I can do with this number.
The first and most obvious is to point out that if, like 96% of the working population, you make less than $109,000 per year, this is because the 4% who is making more than that, is making a lot more. This is what people talk about when speaking of income inequality. It's gotten a bit ridiculous. But there's also a lot of people talking about it, so I'm going to talk about something else.
Remember that population of the earth? 7.13 billion. 7,130,000,000. It's a lot. And remember the total GDP of the USA divided by its population? $53,009. Not bad. I wonder what would happen if you took the collective GDP of the entire planet and divided it by its population? Let's find out.
Again, according to Wolfram Alpha, the GDP of the entire planet is roughly $71.92 trillion. Seems like a lot. Divided by the total number of inhabitants, though, it's only $10,087 per person. Try to remember that all of those dollars are resources. We take resources from the earth and convert them to value, and that's essentially what an economy is. In the United States, each person is roughly entitled to five times the average of the rest of the world. And some countries are far below average. Just something to think about.
In the United States, the population is 319 million. The GDP of the United States is 16.91 trillion. This means that, per person, the total average value produced per year in this country is $53,009. This only gets crazier when you realize that this number is counting all residents, not just those working. According to the U.S. Bureau of Labor and Statistics, the labor force in the United States is right around 155 million. This means that each laborer in this country contributes an average of $109,000 to our economy. Now, there are two things I can do with this number.
The first and most obvious is to point out that if, like 96% of the working population, you make less than $109,000 per year, this is because the 4% who is making more than that, is making a lot more. This is what people talk about when speaking of income inequality. It's gotten a bit ridiculous. But there's also a lot of people talking about it, so I'm going to talk about something else.
Remember that population of the earth? 7.13 billion. 7,130,000,000. It's a lot. And remember the total GDP of the USA divided by its population? $53,009. Not bad. I wonder what would happen if you took the collective GDP of the entire planet and divided it by its population? Let's find out.
Again, according to Wolfram Alpha, the GDP of the entire planet is roughly $71.92 trillion. Seems like a lot. Divided by the total number of inhabitants, though, it's only $10,087 per person. Try to remember that all of those dollars are resources. We take resources from the earth and convert them to value, and that's essentially what an economy is. In the United States, each person is roughly entitled to five times the average of the rest of the world. And some countries are far below average. Just something to think about.
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