My last post was about faith. I'm no closer to having faith, but I'm more comfortable with the idea.
I think that normal people simply see the world in a much more subjective emotional way than I do. They believe in things because it feels right. And that's all there is to it.
That's not a bad thing. John Maynard Keynes wrote about how most business ventures are negative expected value from the get-go, and it requires an irrational belief in the prospects of success (that he called animal spirits) for anything to get started in the first place.
On to utility value. It's a term that basically means how good you think something is. For example a piece of cake has a utility value that's different for everyone, depending on how much you like cake. There's no hard and fast method for determining utility value, but often you can make statements about when something has a higher utility value than something else; for example, we'd all like $200 more than $100.
I've been noticing of late that when people go after stuff, the way they pick what they want involves not only how good the thing is for them, but also the emotional high or low that comes along with getting it. For instance, I really like to save money. I recently saved $5/month on car insurance by increasing our deductible. That's a good thing to do, but it's not great. It's just $5 and isn't going to make me that much happier. I'm happy out of proportion of the true utility value of $5/month (which probably amounts to something extra at the grocery store that I won't really notice). And the same is true for me and others, in lots of different areas in which we judge value: there's this "emotional overlay" on the perceived utility value of stuff that makes us go after stuff that might not be sensible or worth the effort.
I've been applying this by trying to be less anal about stuff. I get happier than I should about keeping my behaviour in a box (bed time, exercise, etc...), so I figure I can optimize my life further by ignoring the urge to panic at 9:50pm when we're not in bed yet.
P.S. Another example of emotional overlay on something that's good but not that good. I'm reading a chess book now that has 607 different examples, divided into various sections. I want to work through this book on a best-effort basis... I want to be able to go through 50 positions and stop. So I wrote a script that randomized the numbers 1 though 607 so I can go in "order" and hop around the book and sample the various sections more or less equally. I seem to have an irrational desire to be in a box.
Wednesday, September 9, 2009
Friday, April 10, 2009
Blogworld, I have a question
I've been reading this book. It's a bunch of short essays about people's personal philosophies and guiding principles.
Unsurprisingly, lots of people talk about faith. Faith in God, faith in humanity, faith in their prospects for success, faith in themselves.
I have a funny thing to tell you about myself. When I tell you, you're going to look at me like a small child who is trying to figure something out. I know this because three different people have given me this look when I explain this to them.
I don't understand faith. I don't have faith in things. To me, faith is a very surprising and foreign concept. It baffles me that faith is something people do.
I want to explain this carefully in order to be understood. When I say I believe something, I mean precisely the following: I have a picture in my head of a pie chart describing all the possible outcomes or explanations for the situation in question. The size of each slice of the pie represents how likely I think it is, as determined by all the information I have. If one of the slices takes up almost the entire pie, then I believe it.
However, faith appears to be a whole different ballgame. From what I understand of faith, the idea is to believe something with certainty, without checking what the actual probability of it is. Or, believing something in spite of what the probability actually is.
The example that came up recently was this: What if The Superhero came down with a terminal illness, and the doctors said that people in her condition died 80% of the time and were cured 20% of the time. Would I have faith that she would be one of the 20% who lived?
I said of course that in that situation I think she has an 80% chance of dying, and a 20% chance of living. The reason is that the doctors' opinions are the best information that I have available. In the absence further evidence, my working theory about this illness would be that The Superhero would most likely die.
The reaction I got was this funny smile that you'd give a child who doesn't understand something very simple.
Since I've been investigating the nature of faith, I've had a few similar conversations. It always leaves me with the creepy feeling of being in a madhouse, like I'm the only sane person left and everyone else has taken temporary leave of their senses.
Let me try to explain how I feel about this with an analogy. A group of intelligent people who's opinion you typically respect are standing around playing with an ordinary 6-sided die. You've been rolling it for a while, and you've gotten each of the numbers 1 through 6 with similar frequency. Then people start talking about what the probability is that the next roll is going to be a 6. You say calmly that the probability of a 6 is about 1 in 6. Everyone looks at you like you've made a very simple and fundamental error in judgment, and they proceed to explain to you that the probability of rolling a 6 on the next roll is nearly 100%. You look at them suspiciously and ask if there's some trick, like they've stuck a magnet or a weight in the die or something to influence the outcome. They maintain the same patronizing smile as they explain that not only have they not messed with the die in some way, but they arrived at the conclusion that the next roll would almost certainly be a 6 specifically by not analyzing how a die works and what is in fact most likely to happen.
This is how I feel. I feel as though some kind of mind control has taken over people who otherwise appear to be sensible most of the time.
So Blogworld, please enlighten me! What is this faith business?
Unsurprisingly, lots of people talk about faith. Faith in God, faith in humanity, faith in their prospects for success, faith in themselves.
I have a funny thing to tell you about myself. When I tell you, you're going to look at me like a small child who is trying to figure something out. I know this because three different people have given me this look when I explain this to them.
I don't understand faith. I don't have faith in things. To me, faith is a very surprising and foreign concept. It baffles me that faith is something people do.
I want to explain this carefully in order to be understood. When I say I believe something, I mean precisely the following: I have a picture in my head of a pie chart describing all the possible outcomes or explanations for the situation in question. The size of each slice of the pie represents how likely I think it is, as determined by all the information I have. If one of the slices takes up almost the entire pie, then I believe it.
However, faith appears to be a whole different ballgame. From what I understand of faith, the idea is to believe something with certainty, without checking what the actual probability of it is. Or, believing something in spite of what the probability actually is.
The example that came up recently was this: What if The Superhero came down with a terminal illness, and the doctors said that people in her condition died 80% of the time and were cured 20% of the time. Would I have faith that she would be one of the 20% who lived?
I said of course that in that situation I think she has an 80% chance of dying, and a 20% chance of living. The reason is that the doctors' opinions are the best information that I have available. In the absence further evidence, my working theory about this illness would be that The Superhero would most likely die.
The reaction I got was this funny smile that you'd give a child who doesn't understand something very simple.
Since I've been investigating the nature of faith, I've had a few similar conversations. It always leaves me with the creepy feeling of being in a madhouse, like I'm the only sane person left and everyone else has taken temporary leave of their senses.
Let me try to explain how I feel about this with an analogy. A group of intelligent people who's opinion you typically respect are standing around playing with an ordinary 6-sided die. You've been rolling it for a while, and you've gotten each of the numbers 1 through 6 with similar frequency. Then people start talking about what the probability is that the next roll is going to be a 6. You say calmly that the probability of a 6 is about 1 in 6. Everyone looks at you like you've made a very simple and fundamental error in judgment, and they proceed to explain to you that the probability of rolling a 6 on the next roll is nearly 100%. You look at them suspiciously and ask if there's some trick, like they've stuck a magnet or a weight in the die or something to influence the outcome. They maintain the same patronizing smile as they explain that not only have they not messed with the die in some way, but they arrived at the conclusion that the next roll would almost certainly be a 6 specifically by not analyzing how a die works and what is in fact most likely to happen.
This is how I feel. I feel as though some kind of mind control has taken over people who otherwise appear to be sensible most of the time.
So Blogworld, please enlighten me! What is this faith business?
Sunday, April 5, 2009
Learning Things I Already Know
In my old age and wisdom, I've come to realize the following:
a) It's better to give than to receive.
b) Raising kids the most challenging and rewarding thing I'll ever do.
c) Lessons mean more when you learn them for yourself.
d) Money is not the most important thing in life.
What I want to talk about today is not these things themselves, but the true nature of this class of knowledge.
These things are examples of what I'd call "canned" statements. You don't have to wait very long in polite company before hearing one of these statements. Making one of these comments confers great honour and nobility upon the speaker.
The tricky thing about these statements is that they're well known and socially acceptable, and they also happen to be true. Furthermore, they would be non-obvious if they weren't cliches: this class of knowledge is the kind of thing that you have to pay to find out. It takes hard work and maturity to understand these things fundamentally.
When someone says something non-obvious and true, it's clear that they must have thought it through. If someone points out that an object near the earth's surface falls approximately 4.9m in the first second, they've either measured it themselves or integrated 9.8 twice from 0 to 1. But with cliche's you can't tell if you're just listening to a parrot or if someone has actually had a fundamental realization about life.
On the upside, though, whenever I do happen to learn one of these things "for real", I get this funny little "aha" moment when I realize that the thing I just learnt maps onto one of those well-known statements. It's something like "Oh, you dopey Mr. Superhero, you're heard that about 50,000 times and you only understand it NOW???".
a) It's better to give than to receive.
b) Raising kids the most challenging and rewarding thing I'll ever do.
c) Lessons mean more when you learn them for yourself.
d) Money is not the most important thing in life.
What I want to talk about today is not these things themselves, but the true nature of this class of knowledge.
These things are examples of what I'd call "canned" statements. You don't have to wait very long in polite company before hearing one of these statements. Making one of these comments confers great honour and nobility upon the speaker.
The tricky thing about these statements is that they're well known and socially acceptable, and they also happen to be true. Furthermore, they would be non-obvious if they weren't cliches: this class of knowledge is the kind of thing that you have to pay to find out. It takes hard work and maturity to understand these things fundamentally.
When someone says something non-obvious and true, it's clear that they must have thought it through. If someone points out that an object near the earth's surface falls approximately 4.9m in the first second, they've either measured it themselves or integrated 9.8 twice from 0 to 1. But with cliche's you can't tell if you're just listening to a parrot or if someone has actually had a fundamental realization about life.
On the upside, though, whenever I do happen to learn one of these things "for real", I get this funny little "aha" moment when I realize that the thing I just learnt maps onto one of those well-known statements. It's something like "Oh, you dopey Mr. Superhero, you're heard that about 50,000 times and you only understand it NOW???".
Wednesday, March 25, 2009
Relativity and Marriage
This is an Emergency Post! I've already posted today, but I just had a conversation with The Superhero that MUST be recorded.
The Superhero is rearranging the living room furniture...
The Superhero: "Do you think the couch will fit between the cabinet and the wall?"
Me: "No way, it's too long."
The Superhero: "Sure it will..." pushes the couch into the spot with room to spare "Ha, there!"
Me: "Well surely that's because it's moving close to the speed of light and it's length is contracted."
The Superhero: "Well if the couch is moving, then we are also moving [since we don't observe it moving] so there would be no length contraction!"
Ha! So, Future Self, as you get older and your body gives out and your mind starts to fade, and you wonder whether it was all worthwhile whether your life was well-spent, remember this: You once had it all. You had a hot 27-year old wife who cooks you pizza, is dirty in bed, and sasses you with Einstein.
You can die a happy man.
The Superhero is rearranging the living room furniture...
The Superhero: "Do you think the couch will fit between the cabinet and the wall?"
Me: "No way, it's too long."
The Superhero: "Sure it will..." pushes the couch into the spot with room to spare "Ha, there!"
Me: "Well surely that's because it's moving close to the speed of light and it's length is contracted."
The Superhero: "Well if the couch is moving, then we are also moving [since we don't observe it moving] so there would be no length contraction!"
Ha! So, Future Self, as you get older and your body gives out and your mind starts to fade, and you wonder whether it was all worthwhile whether your life was well-spent, remember this: You once had it all. You had a hot 27-year old wife who cooks you pizza, is dirty in bed, and sasses you with Einstein.
You can die a happy man.
My Clothes are Getting Lazy
Dear Clothes,
What is going on these days, Clothes? I think you've changed.
I remember a time, not so long ago, when you would cheerfully hop out of the hamper, trot downstairs and tumble into the washer. The jeans would jump in with some detergent, the dress shirts would adjust the dial, and the sweaters would close the lid.
You were such a great team, Clothes. The underwear would keep an eye on the socks so they wouldn't escape from the dryer, and the T-shirts would comfort the pajama pants during the spin cycle. You had a buddy system for the trip from the washer to the dryer, and you all had such a great time tumbling around together.
Then you'd parade back upstairs, marching in proud, clean lines, to find your homes again on hangers and in drawers.
I never actually saw this process, but I assume that's how it must have happened. The stained, wrinkled heap of old clothes magically reappeared nicely folded and hanging ready to serve again.
But Clothes, you have changed. You are despondent and depressed, laying around in the hamper for days. You ignore your dirt, your creases, your odors, and do nothing about it. Is it something I said? Something I did? Have I not paid enough attention to you, Clothes?
Now I must haul you down to the washer myself, move you from washer to dryer to basket to drawer without any help from you, Clothes. What has happened to you, Clothes?
Sincerely,
Mr. Superhero
P.S. Clothes, it doesn't have anything to do with this, does it?
What is going on these days, Clothes? I think you've changed.
I remember a time, not so long ago, when you would cheerfully hop out of the hamper, trot downstairs and tumble into the washer. The jeans would jump in with some detergent, the dress shirts would adjust the dial, and the sweaters would close the lid.
You were such a great team, Clothes. The underwear would keep an eye on the socks so they wouldn't escape from the dryer, and the T-shirts would comfort the pajama pants during the spin cycle. You had a buddy system for the trip from the washer to the dryer, and you all had such a great time tumbling around together.
Then you'd parade back upstairs, marching in proud, clean lines, to find your homes again on hangers and in drawers.
I never actually saw this process, but I assume that's how it must have happened. The stained, wrinkled heap of old clothes magically reappeared nicely folded and hanging ready to serve again.
But Clothes, you have changed. You are despondent and depressed, laying around in the hamper for days. You ignore your dirt, your creases, your odors, and do nothing about it. Is it something I said? Something I did? Have I not paid enough attention to you, Clothes?
Now I must haul you down to the washer myself, move you from washer to dryer to basket to drawer without any help from you, Clothes. What has happened to you, Clothes?
Sincerely,
Mr. Superhero
P.S. Clothes, it doesn't have anything to do with this, does it?
Wednesday, March 11, 2009
This and That
One of my goals in starting a blog was to capture the state of my life at various points so they don't drift off into the foggy blur of old memories. So today I'm going to write about a bunch of random stuff that's going on right now.
- The monkeys are at a great age right now (1.5/3/4/4). The Superhero set up the basement a couple of weekends ago for to be kid-friendly, and they're actually using it independently some of the time. About a year and a half ago I remember the transition when we went from having to do basic housework when everyone was sleeping to being able to do some of it when the kids were awake. Now we're transitioning to being able to do grown-up things while the kids are awake. It's great. Last Saturday we had sex twice in the morning while the kids played on the main floor.
- On that note, The Superhero has been very amourous lately; sans any kind of reading material that might influence her in that direction. I thank hormones, helped along by the recent egg donation.
- The kids getting old enough to just about understand some things. They know that I go to work to make money, and we use it to buy food. I tried to explain taxes the other day, but it didn't go over so well.
- I'm on a physics kick recently. I just worked out the speed of a small "wobble" in a disk as compared to the speed of rotation of the disk. Turns out the disk wobbles at twice the speed of the disk's rotation for small wobbles. It follows from setting up the equations for the position of any particle at any time, differentiating to get speed and acceleration, and then requiring that the angular momentum is constant since there's no outside torques. I'm now reading the popular version of the theory of relativity by Einstein. I tried the real version (with all the math details) and it became so dense that I switched to the softer one, sadly. It's the neatest physics problem there will probably ever be, since:
- It's very simple: consider that non-accelerating frames of reference are indistinguishable, and that the speed of light is constant. The whole problem is: if these two things are true, what are the implications? (the apparent paradox is that if you walk away from me and I shine a flashlight at the speed of light, you'd think that you'd observe the light going at the speed of light less the speed of you're walking, but we said the speed of light is constant and each frame of reference is equivalent for judging that, so you actually also see the light going at the speed of light!)
- The subject is things that are more or less part of our everyday experience (trains, embankments, etc.). It's not like particle physics where the trick is imagining what tiny things we've never see are like.
- The whole trick is questioning the simplest things we depend on (like our conceptions of space and time), and remembering what you can still think and what is wrong. Very tricky!
Monday, March 2, 2009
The Nature and Limits of Scientific Investigation
I've spent most of my spare time since my last post thinking about Problem #3, and trying, mostly unsuccessfully, to torture The Superhero with it as well. I'm happy to report that I now understand the jump between the fuzzy fog inside my head and the math laws that describe reality.
Today I'm going to explain the nature of how we understand our world and what limitations are in how we can describe it. I'm also going to try to explain this in a lay-person-accessible way; I like the challenge of explaining complicated things in ways that make sense to people not acquainted with the details of the problem, and it's a good test for how well I understand things.
First, let's recap the problem. Suppose you and I are trying to measure the length of a piece of string. We'd hold the string up against a yardstick and argue back and forth about how long it is. I think it's 19.4 inches, and you think it's 19.6 inches. We decide in order to break the tie we're going to get a yardstick with ticks every 1/4 of an inch, and measure again. It turns out it's a bit on the long side of 19.5 inches, so you're closer to the right answer. But suppose I'm difficult and insist that it's not 19.6 inches: I say it's 19.58 inches. You can see this could go on for a while, getting ever-more precise yardsticks and eventually requiring magnifying glasses and microscopes to tell who's right. Still we could go on and on forever, never agreeing on the exact length, until we get down to the molecular level and we'd start arguing where the "end" of the string is in on the frayed end of the string.
To state the problem succinctly, our perceptions are foggy, and subject to interpretation. When we observe something, you and I will not necessarily agree on the measurement. So how do we make laws about the world? When we say a toothbrush falls at a constant acceleration of 9.8m/s2, what do we mean exactly, and how can we measure it in a way we can agree on?
So thinking about this, I the first thing I did was study myself looking at stuff, observing what the problems were that stop me from understanding what I'm seeing in a well-defined way that I can make rules about. I noticed 3 things:
Unreliability can be gotten around as well. The unreliability in my perceptions can be gotten around by using measurement devices that start out in exactly the same state. I could build a reliable thermometer that will always report the same temperature in the same way.
The core problem with us agreeing on the how long the string is, is the fact that our perceptions come to us in a way that's not formally defined. We can never decide exactly where the end of the string is; we think it's about 19.5 inches, but we can't decide because we both have this estimation that's going on inside our heads that comes out slightly differently.
The key to understanding how this works clearly, is that our brains are also part of the physical world, and in this case are forming part of the experiment. On close examination, it's clear that I am making a direct and exact measurement of the physical world, but the measurement is not just a function of the string. It's a function of everything. It's a function of the psychological estimation procedure in which I guess the end of the string is about 4/10 of the way between the 19 inch line and the 20 inch line. It's also a function of how the gravitational attraction from between the string and my brain stretches the string toward my head. It's also a function of the tides of the Pacific Ocean and how that water is pulling the string. The measurement device, and everything else in the universe, contributes towards getting the number 19.4. However, 19.4 is completely function of the real world, not a concoction of some mystical "consciousness" that's actually just a configuration of atoms in my brain.
If you don't want to measure anything about your psychology, you can pass your brain information from the outside world in a way that doesn't need interpretation. That is, you can make a measurement device that has a little display that shows you numbers, or little blinking lights that lend themselves to a non-fuzzy interpretation. So if your thermometer says 8 degrees, you and I can look at that and agree exactly what it says. The measurement is still a function of not only the ambient temperature but also of the thermometer (for instance, how it rounds the temperature off to 8 degrees). It's also technically a function of your brain, since maybe the thermometer says 18 degrees and you just missed the 1. But assuming we can read the device without error, we'll all agree on what it says.
So far so good. Despite the 3 weaknesses of how information comes into my brain when I hold a banana and look at it, these can be overcome and I can get direct, well-defined measurements of the physical world that I can then get to work on making rules about. I can put out my digital thermometer, take periodic readings, and try to notice patterns in how the temperatures change with the seasons and make scientific discoveries. Furthermore, I can create any kind of coccamamy ideas in my head to explain it, and they're all equally good, provided that they predict my observations correctly.
However this does not totally answer the questions of how we can conduct science. Suppose I come up with some law that describes how the temperature changes with the seasons. This is only a description of what my thermometer read at various times and rules about how the readings relate to each other. When someone else tries to interpret that and reproduce my results, he'll come up with some experimental setup that looks kind of like mine, but isn't quite the same. And we'll be back in the same position we were in trying to measure the string; I can't describe exactly how to reproduce the conditions of my experiment so that the readings off the next guy's digital thermometer measure the exact same thing as mine did.
So in conclusion, we can say the following about the physical laws (rules) we make up to describe our world:
P.S. Through this train of thought I've come up with a much more important question. How on earth do we manage to have such success in the world by making judgements on perceptions that can't be tested for whether they follow rules? Unfortunately, this is a question for psychology and neuroscience to answer. You can't figure it out just by thinking.
Today I'm going to explain the nature of how we understand our world and what limitations are in how we can describe it. I'm also going to try to explain this in a lay-person-accessible way; I like the challenge of explaining complicated things in ways that make sense to people not acquainted with the details of the problem, and it's a good test for how well I understand things.
First, let's recap the problem. Suppose you and I are trying to measure the length of a piece of string. We'd hold the string up against a yardstick and argue back and forth about how long it is. I think it's 19.4 inches, and you think it's 19.6 inches. We decide in order to break the tie we're going to get a yardstick with ticks every 1/4 of an inch, and measure again. It turns out it's a bit on the long side of 19.5 inches, so you're closer to the right answer. But suppose I'm difficult and insist that it's not 19.6 inches: I say it's 19.58 inches. You can see this could go on for a while, getting ever-more precise yardsticks and eventually requiring magnifying glasses and microscopes to tell who's right. Still we could go on and on forever, never agreeing on the exact length, until we get down to the molecular level and we'd start arguing where the "end" of the string is in on the frayed end of the string.
To state the problem succinctly, our perceptions are foggy, and subject to interpretation. When we observe something, you and I will not necessarily agree on the measurement. So how do we make laws about the world? When we say a toothbrush falls at a constant acceleration of 9.8m/s2, what do we mean exactly, and how can we measure it in a way we can agree on?
So thinking about this, I the first thing I did was study myself looking at stuff, observing what the problems were that stop me from understanding what I'm seeing in a well-defined way that I can make rules about. I noticed 3 things:
- My perceptions are incomplete. I see some things and not others. For instance, I don't see x-rays.
- My perceptions are unreliable. That is, I perceive the same thing in two different ways if it happens to me twice. For instance, when I wake up, things are much brighter than when I come in from out in the sun
- My perceptions are undefined. This means that the lower levels of my brain that take the stimulation from my eyeball and turn it into a meaningful picture for me present it to my higher-level consciousness don't present that picture in a way I can write down and communicate clearly. For instance, when I look at two pieces of art and one looks nice and one does not, I can't describe to you every detail of why I think that's so.
Unreliability can be gotten around as well. The unreliability in my perceptions can be gotten around by using measurement devices that start out in exactly the same state. I could build a reliable thermometer that will always report the same temperature in the same way.
The core problem with us agreeing on the how long the string is, is the fact that our perceptions come to us in a way that's not formally defined. We can never decide exactly where the end of the string is; we think it's about 19.5 inches, but we can't decide because we both have this estimation that's going on inside our heads that comes out slightly differently.
The key to understanding how this works clearly, is that our brains are also part of the physical world, and in this case are forming part of the experiment. On close examination, it's clear that I am making a direct and exact measurement of the physical world, but the measurement is not just a function of the string. It's a function of everything. It's a function of the psychological estimation procedure in which I guess the end of the string is about 4/10 of the way between the 19 inch line and the 20 inch line. It's also a function of how the gravitational attraction from between the string and my brain stretches the string toward my head. It's also a function of the tides of the Pacific Ocean and how that water is pulling the string. The measurement device, and everything else in the universe, contributes towards getting the number 19.4. However, 19.4 is completely function of the real world, not a concoction of some mystical "consciousness" that's actually just a configuration of atoms in my brain.
If you don't want to measure anything about your psychology, you can pass your brain information from the outside world in a way that doesn't need interpretation. That is, you can make a measurement device that has a little display that shows you numbers, or little blinking lights that lend themselves to a non-fuzzy interpretation. So if your thermometer says 8 degrees, you and I can look at that and agree exactly what it says. The measurement is still a function of not only the ambient temperature but also of the thermometer (for instance, how it rounds the temperature off to 8 degrees). It's also technically a function of your brain, since maybe the thermometer says 18 degrees and you just missed the 1. But assuming we can read the device without error, we'll all agree on what it says.
So far so good. Despite the 3 weaknesses of how information comes into my brain when I hold a banana and look at it, these can be overcome and I can get direct, well-defined measurements of the physical world that I can then get to work on making rules about. I can put out my digital thermometer, take periodic readings, and try to notice patterns in how the temperatures change with the seasons and make scientific discoveries. Furthermore, I can create any kind of coccamamy ideas in my head to explain it, and they're all equally good, provided that they predict my observations correctly.
However this does not totally answer the questions of how we can conduct science. Suppose I come up with some law that describes how the temperature changes with the seasons. This is only a description of what my thermometer read at various times and rules about how the readings relate to each other. When someone else tries to interpret that and reproduce my results, he'll come up with some experimental setup that looks kind of like mine, but isn't quite the same. And we'll be back in the same position we were in trying to measure the string; I can't describe exactly how to reproduce the conditions of my experiment so that the readings off the next guy's digital thermometer measure the exact same thing as mine did.
So in conclusion, we can say the following about the physical laws (rules) we make up to describe our world:
- All observations we make that somehow get translated into a well-defined thought are exact physical measurements about our world, including our brain. By constructing our measurements in clever ways, we can limit the impact that our brain and other irrelevant effects have on measuring, but results will always be a function of everything.
- The theories we invent to explain the world, exist solely within our brains. We might make predictions based on a theory of electrons, and an alien race might make identical predictions with no concept of electrons, and we can both be equally right. The only test of the theory is does it predict measurements properly.
- The interpretation of how to make the measurement to test against the theory is fundamentally dependent on human interpretation. There is no way to describe a theory in which two people will make measurements to test it in precisely the same way and never disagree. By describing measurement techniques you can get people to agree more often and measure in more similar ways; but you will never get them to agree 100% of the time.
P.S. Through this train of thought I've come up with a much more important question. How on earth do we manage to have such success in the world by making judgements on perceptions that can't be tested for whether they follow rules? Unfortunately, this is a question for psychology and neuroscience to answer. You can't figure it out just by thinking.
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