There are tons of articles out there that address this question. I realize that anything I write, with the awkward style that I can't seem to improve on, would add little value to the wealth of resources on the internet. Yet, I really want to write about this. I realized that this blog of mine is more a journal than it is a blog- about 1% of all the views it has come from myself, and I find it quite interesting, or amusing, or even embarrassing, to read things I wrote a few years ago. It's like looking at a stupider version of myself. It makes me feel good that I didn't stay that stupid later on.
Anyways, that little "Note to self" aside,
What is science?
Different people refer to different things when they say "science". Even I refer to different things at different times, and sometimes different things AT THE SAME TIME.
Sometimes, the word "science" refers to the body of scientific literature. All of the conjectures, hypotheses, and theories that are currently accepted to be sensible. Sometimes it also includes hypotheses that we, today, say are invalid. The geocentric theory, for instance, is sometimes considered part of science- but we all know today that celestial bodies do not revolve around the earth.
And at other times, the word "science" refers to the scientific method. One phrase I love using is, "Let's do some science". It carries that feeling of adventure, of invention, and of altruism, the excitement that goes with doing something that no one has done before, knowing something unknown to the rest of humanity.
When one says, "We are doing science", they are referring to the scientific method, not the body of literature.
But then again, not everything that follows the scientific method is called science. Learning to hit a target with a projectile isn't called a science, although the mind does do a bit of experimentation, a bit of modeling, and in the end produces skill in being able to predict and control projectile motion. No, "science" requires more rigor. More data. MORE MATH.
And this is what makes me embrace this definition for science:
Science is the practice of mapping the physical world to the mathematical world.
I don't remember who said that, but this definition for science is the one I've been using for quite some time now. The scientific method helps identify the right mapping, and the scientific literature is the collection of maps.
With my definition for science, three things become clear:
1) If a "hypothesis" does not involve mathematics, it cannot be science.
2) It pisses me off when someone says "I came up with this super cool theory, and it doesn't even need math." I'm sorry, but if there's no math in there, it's not worth squat.
3) Mathematics has a special, some might call it mystical, connection to the physical world.
(Note: There are the so-called "soft sciences" that don't involve much precise math. Medicine, for instance. I don't think that these sciences don't involve math. Rather, the complex dynamics of these systems make the math so hard that we are simply not competent enough to deal with it.)
The first consequence makes sense. After all, one of the biggest motivations for doing science is the ability to make predictions. And except for the most mundane things, predictions involve math.
The second, well that's a given. We wouldn't need to spend billions of dollars on funding mathematicians, and building super computers, if all it took to understand the universe was for little Johnny to scribble some ignorant non-sense on a piece of paper.
The third one, that's quite philosophical. I guess it's obligatory to cite this article here: The unreasonable effectiveness of mathematics in the natural sciences
Why math? What's special about it? And, this is where it gets interesting, WHAT IS MATHEMATICS?
People have different definitions for math too. And, again, the one I embrace is:
The art of (finding) (non-trivial) tautologies.
That's all I can think of when I try to understand what math is. You start with a bunch of axioms, and you use logic to arrive at non-trivial conclusions. Well well well.. And what exactly is logic? (shit just got real)
Let's see. Logic is a consequence of language, it's the practice of mapping "statements with the same meaning" to one another. Again, that's how I choose to understand logic.
So, this is what I understand of what we're doing:
We have two, apparently separate, worlds.
1) The natural world that just does its thing without caring for our desire to understand it.
And
2) The mathematical world, which is a huge collection of statements that all, after loads of manipulation, mean the same things as a small set of statements put together (the axioms).
Some of the greatest geniuses of our species devote decades to find more statements that mean the same thing as others we are interested.
And some of the other geniuses devote decades to map things in the natural world to something in the mathematical world- either to the axioms directly, or something derived from the axioms.
As long as the axioms are sensibly chosen, and the mapping from the natural to the mathematical world is well-made, we can make all sorts of predictions- thanks to all those mathematicians who have already worked thousands and thousands of things that follow.
And this leads to the question that's really been bugging me- can we come up with a better math?
After all, all we need is a set of consistent axioms, and a mapping from the physical to this new mathematical world. Is our math the ONLY possible math? Is there a better math "out there" that can do a better job at explaining nature? Would artificial intelligence be able to come up with different maths than we did?
If there are different sorts of math that can explain nature, which one do we hold? The best one? The worst one? A mediocre one? Supposing there's an intelligent alien life a few thousand light years away, could they have identified a better math?
Bonus reading: The reasonable ineffectiveness of mathematics
Anyways, that little "Note to self" aside,
What is science?
Different people refer to different things when they say "science". Even I refer to different things at different times, and sometimes different things AT THE SAME TIME.
Sometimes, the word "science" refers to the body of scientific literature. All of the conjectures, hypotheses, and theories that are currently accepted to be sensible. Sometimes it also includes hypotheses that we, today, say are invalid. The geocentric theory, for instance, is sometimes considered part of science- but we all know today that celestial bodies do not revolve around the earth.
And at other times, the word "science" refers to the scientific method. One phrase I love using is, "Let's do some science". It carries that feeling of adventure, of invention, and of altruism, the excitement that goes with doing something that no one has done before, knowing something unknown to the rest of humanity.
When one says, "We are doing science", they are referring to the scientific method, not the body of literature.
But then again, not everything that follows the scientific method is called science. Learning to hit a target with a projectile isn't called a science, although the mind does do a bit of experimentation, a bit of modeling, and in the end produces skill in being able to predict and control projectile motion. No, "science" requires more rigor. More data. MORE MATH.
And this is what makes me embrace this definition for science:
Science is the practice of mapping the physical world to the mathematical world.
I don't remember who said that, but this definition for science is the one I've been using for quite some time now. The scientific method helps identify the right mapping, and the scientific literature is the collection of maps.
With my definition for science, three things become clear:
1) If a "hypothesis" does not involve mathematics, it cannot be science.
2) It pisses me off when someone says "I came up with this super cool theory, and it doesn't even need math." I'm sorry, but if there's no math in there, it's not worth squat.
3) Mathematics has a special, some might call it mystical, connection to the physical world.
(Note: There are the so-called "soft sciences" that don't involve much precise math. Medicine, for instance. I don't think that these sciences don't involve math. Rather, the complex dynamics of these systems make the math so hard that we are simply not competent enough to deal with it.)
The first consequence makes sense. After all, one of the biggest motivations for doing science is the ability to make predictions. And except for the most mundane things, predictions involve math.
The second, well that's a given. We wouldn't need to spend billions of dollars on funding mathematicians, and building super computers, if all it took to understand the universe was for little Johnny to scribble some ignorant non-sense on a piece of paper.
The third one, that's quite philosophical. I guess it's obligatory to cite this article here: The unreasonable effectiveness of mathematics in the natural sciences
Why math? What's special about it? And, this is where it gets interesting, WHAT IS MATHEMATICS?
People have different definitions for math too. And, again, the one I embrace is:
The art of (finding) (non-trivial) tautologies.
That's all I can think of when I try to understand what math is. You start with a bunch of axioms, and you use logic to arrive at non-trivial conclusions. Well well well.. And what exactly is logic? (shit just got real)
Let's see. Logic is a consequence of language, it's the practice of mapping "statements with the same meaning" to one another. Again, that's how I choose to understand logic.
So, this is what I understand of what we're doing:
We have two, apparently separate, worlds.
1) The natural world that just does its thing without caring for our desire to understand it.
And
2) The mathematical world, which is a huge collection of statements that all, after loads of manipulation, mean the same things as a small set of statements put together (the axioms).
Some of the greatest geniuses of our species devote decades to find more statements that mean the same thing as others we are interested.
And some of the other geniuses devote decades to map things in the natural world to something in the mathematical world- either to the axioms directly, or something derived from the axioms.
As long as the axioms are sensibly chosen, and the mapping from the natural to the mathematical world is well-made, we can make all sorts of predictions- thanks to all those mathematicians who have already worked thousands and thousands of things that follow.
And this leads to the question that's really been bugging me- can we come up with a better math?
After all, all we need is a set of consistent axioms, and a mapping from the physical to this new mathematical world. Is our math the ONLY possible math? Is there a better math "out there" that can do a better job at explaining nature? Would artificial intelligence be able to come up with different maths than we did?
If there are different sorts of math that can explain nature, which one do we hold? The best one? The worst one? A mediocre one? Supposing there's an intelligent alien life a few thousand light years away, could they have identified a better math?
Bonus reading: The reasonable ineffectiveness of mathematics
