Math is the metaphysics of science. Every scientific discovery is the discovery of a mathematical pattern in the world.
To tell a mathematical story of the world that people can grow up with, we need to start with games we can show to preschoolers to help them visualize the fundamental mathematical patterns in the world. As they get older they can use what they learned from their game to understand the world better.
The scientific story of the world only depends on 4 mathematical laws that you can demonstrate with building blocks.
ACT I
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Gym class is also known as physical education. So what’s metaphysical education?
Math class.
Math is the metaphysics of science. But how you look at the math depends on what you want to use science for.
If you think of science as a job skill, you want to know specifically what the numbers say. But is that the only way we use math and science?
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Science shows us patterns in the world that correspond to patterns in math. Now that scientists have done the math and discovered the patterns, we can just talk about the patterns. Ideas that change how you look at the world are philosophical ideas, including scientific discoveries.
You’re using electricity to listen to me right now. You know that lighting is electricity, and you know that thunder is the sound of lightning heating air very quickly.
Think about this. You know a lot more about lightning than people did back when they were trying to guess what it was. But how much do you need to know about the history of the math involved in the discovery of electricity to understand what electricity is?
If you teach science as if you’re trying to teach people to be scientists, many people won’t be interested because they don’t want to be scientists. Many people won’t be interested because they aren’t good at math. But if you think about science in terms you can explain to three and four year olds, you make it accessible to everyone.
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Math begins with counting. That means you can illustrate the simplest patterns in math with building blocks.
You’d have to tell three year olds this stuff more than once, like you have to tell them everything more than once, to get them to remember it. But if you can turn numbers into a game, they’ll keep playing the game and remember it, without realizing it’s a lesson for life.
All learning is building blocks in a way. In every moment of your life what you learn is built atop everything else that’s happened in your life to that point. Ask your teachers about the building block model of education and hear what they say.
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The story of Being Human on Planet Earth only depends on four mathematical laws. I call them zero, one, two, and three.
Here we go again, mixing classes together. This could be math, or it could be philosophy, or it could be English class, because we’re talking about the meanings of words. It isn’t any one of them. It’s all of them at once.
What makes these four laws so important to the story isn’t that they’re complicated. What makes them so important is that they’re so simple they’re easy to forget sometimes, even though they’re always true.
The first two laws are definitions of words we use to compare numbers. The second two are about relationships that make numbers either change or stay the same.
ACT II
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General Mathematical Law #0: Constant = Constant.
Something that stays the same always works the same way. I call this the Zeroeth Mathematical Law because it isn’t much of a discovery. But it is important to remember because sometimes people forget.
Mathematical and scientific laws always work the same way. Even for you. If you jump off the roof of a building with an optimistic attitude, you’ll fall just as fast as if you jumped off it with a pessimistic attitude, or with any other attitude, and fall just as fast as anyone else would fall. Or to put this in pandemic terms, Covid doesn’t care whether you believe in it or not.
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What’s the building block version of Constant = Constant? Put two blocks on a table and look at them without touching them. How long would you have to look at the blocks to make them move?
Looking at blocks doesn’t make them move. If nothing changes them, they don’t change.
ACT III
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General Mathematical Law #1: Finite = Finite.
A number that can’t be increased or decreased always stays the same. The First Mathematical Law is a lot like the Zeroeth Mathematical Law, except that instead of talking about general principles we’re talking about specific quantities.
This is the math behind the First Law of Thermodynamics. Matter and energy are never created or destroyed. They only change form.
That means the energy content of the universe is finite. The energy content of the sun is finite. The matter on Earth is finite. Even though the Earth gets energy from the sun, that’s finite.
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We got into the environmental crisis because people confused more than we can imagine using up with infinite.
If you walked into a forest the size of North America all by yourself with an axe, the trees there would be essentially infinite. You would die of old age before you could cut them all down.
But if more people kept coming into the forest and bringing more powerful tools for cutting down trees, eventually your infinite supply of trees would stop being infinite.
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The Earth isn’t infinitely large. It’s 25,000 miles around at the equator. Anyone who promises you an unlimited supply of anything is lying.
That includes unlimited space for pollution. So when anyone talks about an endless supply of anything, the question is always: When is it going to run out, and what’s going to happen when it does?
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What’s the building block version of Finite = Finite?
Put five or six blocks on the table and ask your preschooler to count them. Then move them around and ask them to count them again. Ask them to put them in any pattern they want, and count them again. As long as no one adds any blocks or takes any away, there will always be the same number you started with.
Bert and Ernie did this experiment with cookies on Sesame Street.
ACT IV
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General Mathematical Law #2: Change = Motion.
If something is moving it means it’s changing. Motion is change relative to a place. If something is changing it means it’s moving, or some part of it is moving.
The universe is made of energy and matter. If something is changing it means one way or another it’s gaining or losing energy, matter, or both.
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This is the math behind the Second Law of Thermodynamics.
This is the mathematical relationship that’s making the universe expand. It’s easy to find examples of it, because it’s all around us all the time. But it can be hard to believe that they’re all examples of the same mathematical law, because it plays out on different scales, from the smallest things you can see to the biggest things you can see, and everything in between.
Let’s say you make a pot of soup. Then you pour some salt into a teaspoon. You drop the salt into the soup, and you stir it in.
On another scale, you just made the entire lifespan of the universe happen.
Everything in the universe is moving. A high concentration of something
means the number of places the thing could be is larger than the number of places it is now. So when things move they tend to spread out. Some of them move into places they weren’t in before, unless something prevents them.
To be more specific, we can say that matter and energy move from high concentration to low concentration more than they move from low concentration to high concentration. Motion is always mostly from high concentration toward low concentration. Another way to say that is disorder tends to increase.
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You started with pure salt in a teaspoon. Then you dropped the salt into the pot and stirred it— meaning, you added kinetic energy to it. Now the salt is spread through the pot, mixed with the soup.
The energy made the salt spread out into more places than it was in before, and now it isn’t a pure concentration. No matter how much you stir your soup now, you can never make all the salt come back to your spoon. Because motion is mostly from high concentration toward low concentration.
In the same basic way, the universe began with highly concentrated energy, which reached a critical mass about 14 billion years ago and exploded in theBig Bang. Now almost all the other galaxies are moving away from us, as if we’re grains of salt being stirred into a pot of soup.
Ask your physics teacher about that, and they’ll be glad to explain it to you.
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Why does everything wear out eventually?
When you buy a new pair of shoes, all the shoe molecules start out connected to your shoes. Then the more you wear your shoes, the more you wear them out.
When you walk around friction makes molecules break off your shoes. You don’t notice it, but everywhere you walk you leave behind a trail of molecular dust that used to be part of your shoes.
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Why does your bedroom get messy?
A clean room is an arrangement among things. A clean room is one where everything is in an ideal place. If you put all your things back where they belong, your room stays clean.
If you don’t put things back where they belong, it gets messy until you do put them back where they belong. But putting things back where they belong takes more energy than putting them down wherever you happen to be at the moment and leaving them there.
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Why do people die?
A living body is a collection of molecules that interact in a continuous pattern. Whether by old age, disease, accident, murder, war, starvation, or any other cause, anything that makes people die disrupts that pattern. It makes some of the molecules leave the pattern without being replaced with more molecules that keep the pattern going. That makes the pattern of life end, and the person dies.
Since we depend on order to live, we seek order and create order without even noticing. It’s easy for us to not notice how much disorder is possible.
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Here’s another experiment you can try.
Get a deck of playing cards. Then arrange the deck by suit and by number. Each of the 52 cards is now in a specific place in the deck. Let’s say the Ace of Spades is the top card, the King of Spades is second, the Queen of Spades is third, and so on.
Now shuffle the cards. Your order is gone, replaced by disorder.
Now take a guess. How many times would you have to shuffle the cards to be able to get every possible combination once? Shuffling the cards at random would mean you’d get some combinations two or more times before you got every combination once, but let’s ignore that. What’s the minimum number of times you would have to shuffle the deck to get every possible combination?
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There are 52 cards. The Ace of Spades started out on top, and there are 52 places it could end up.
That means the King of Spades could end up in 51 different places— because it can’t end up in the same place as the Ace of Spades. The Queen of Spades could end up in any of 50 positions. And so on.
That gives you 52 x 51 x 50… and so on, all the way down to 3 x 2 x 1.
That’s a gigantic number. You’ll need a computer to calculate it, because there aren’t nearly enough spaces on a calculator.
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How long would it take to shuffle the cards that many times?
Let’s say it takes you 15 seconds to shuffle the cards. Fifteen seconds is four shuffles per minute. So start with the number of times you’d have to shuffle the cards, ÷ 4 shuffles per minute ÷ 60 minutes per hour ÷ 24 hours in a day ÷ 365.25 days in a year, gives you the number of years it would take.
That’s still a gigantic number. So let’s take one more step and look at it another way.
Divide that gigantic number of years by 14 billion to see how many times the lifespan of the universe would have to happen for you to shuffle your deck of cards enough times to be able to get every result once.
It’s still a gigantic number.
So remember, every time you pick up a deck of cards you’re holding a mathematical law in your hand that’s more powerful than the entire universe. So you better pay attention to it, because you can’t wish it away.
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This is another clue why the environmental crisis is happening.
People think of order as normal because we depend on order to live. They didn’t realize how much disorder was possible.
That’s why it’s hard to believe that you can watch the mathematical law that’s making the entire universe move every time you put salt in your soup or sugar in your coffee.
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How can you see Change = Motion with building blocks?
One way is to line some blocks up on the table and push another block past them with your finger. You can see how the block is moving by how its position is changing in relation to the other blocks. Motion is change relative to a reference point.
Change and motion are what create the variables in science. To measure how they change we have to compare them to constants.
How can you use blocks to see how disorder tends to increase?
They sell that game at the store. That’s what Jenga is.
The blocks start out concentrated neatly in the Jenga tower. Then you take a block from the bottom and you put it on top, you take a block from the middle and you put it on top. When someone moves a block and makes the tower fall over, they come crashing down all over the table.
ACT V
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General Mathematical Law #3: Stability = Balance.
Since everything is moving, and movement means change, whenever something is staying the same it means that moving things have settled into a pattern.
A rock is a very stable pattern of molecules. The electrons are orbiting the nuclei of the atoms, you can pick up the rock and move it, and the planet the rock is on is moving. But the molecules in the rock are connected to each other in a very stable pattern.
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A river is a stable pattern that’s caused by gravity and the shape of the landscape affecting water molecules.
Rain falls on sloping ground, the water runs downhill, it collects into streams, the streams feed into a river, and the river runs to the ocean. But the river depends on water evaporating somewhere, and condensing into raindrops over that landscape. If that stops happening, the river dries up.
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You are a stable pattern of energy and molecules interacting with each other. Or we could say that the energy and molecules make up patterns that make up larger patterns, and larger patterns, and so on, and you are the big pattern they make.
If something takes some critical energy or molecules out of the pattern without replacing them, the pattern ends and you die. But as long as that doesn’t happen, the pattern continues and you keep living.
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A stable environment is a very big pattern made up of many smaller physical, chemical, and biological patterns. We get energy from the sun, water evaporates and condenses, rain falls, streams and rivers run to the ocean, lots of plants and animals get the matter and energy they need to live from processes like those, and their lifecycles fit together into food webs.
Another reason we got into the environmental crisis is because people didn’t notice how much balance there was in the world. We think of balance, or order, as normal, because we depend on balance to live. So it took us a long time to notice how much balance we were destroying.
Now the climate crisis is upon us because we’ve thrown the climate so far out of balance that it’s affecting us.
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What’s a building block version of Stability = Balance?
One thing you can do is to see how tall of a tower you can build. As long as all the blocks in the tower stay in balance, your tower stays up. That means it’s stable.
If you want to see motion turn into stability, you can push a block around on the table with your finger. Then have your preschooler push a block around with their finger. Then push the blocks up against each other and keep pushing them.
You’re both still pushing your blocks like you were before, but now that you’re pushing them against each other they aren’t moving anymore. You’d get the same thing if you push on opposite sides of the same block. Or if you each push on your own blocks with another block or two in between them.
ACT VI
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Science depends on math. That means people can only understand science to the point they can visualize the mathematical relationships involved.
Lightning, or electricity in any form, is caused by electrons building up inone place and then spreading out into a place with fewer electrons. Change = Motion.
To understand what science shows about the origins of the universe, the Earth, the environment, and people, and how people and the environment function and interact with each other throughout history, today, and into the future, you need to understand four basic relationships among numbers.
Constant = Constant
Finite = Finite
Change = Motion
Stability = Balance
What always stays the same? How much is there? How are things moving, and how are things changing? How do things that are moving and changing run into each other, stabilize, and balance each other out?
If you can visualize yourself teaching these four simple things to a preschooler, it means you understand them.
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Almost all of our mayors, Representatives, Senators, Governors, and Presidents graduated from college. If they can’t understand these things, that should be your first clue that there’s something seriously wrong with our education system!
Now here’s the hard part. These are mathematical laws. That means they’re true all the time. Are you prepared to believe that? Even when you wish they weren’t?
That’s the difference between learning something and misunderstanding it.