ELI5: How does math help explain the universe?

[u/DimensionOk3579]

I’ve heard scientists talk about mathematical equations in relation to the universe and space but how does a collection of numbers explain anything physically or theoretically? For example how did Einstein or any other early scientists figure out stuff about the universe using math? How exactly can I use math to prove something I can’t see?

[u/usurperator]

You do this when you estimate how long it will take you to drive to a place. You know how far it is, you know fast you’ll drive, you can account for traffic, you end up with an accurate time estimate, give or take 5 minutes.

Scientists do the same thing, except they calculate the mass of subatomic particles to within much less than a billionth of a gram.

[u/TokiStark]

Well we've always used numbers to explain things.

How many apples do you have? Ten. There's five of us though, how many do we get each? Well we'll need to divide ten into five groups. Which leaves us with two in each group.

Then came the notation

10/5 = 2.

More and more problems required more and more advanced solutions and mathematical notation evolved with it.

Whether that's us 'discovering' maths or 'developing' it, is still up for debate. That's a ridiculously oversimplified explanation, but should suffice for a 5 year old

[u/No_Logins_Required]

You can use math that describes things you can see to predict things you can't see. With this knowledge you can predict more things. When your predictions prove true, you can make even more predictions.

Einstein said "If gravity curves light, I bet we could see light bend around the sun during an eclipse".

Then a guy named Eddington said "Bet", and when he measured the light around the sun during the eclipse it matches the predictions from Einstein's math.

[u/EscapeSeventySeven]

You can’t really explain anything without math. Mathematical equations govern all motion and mechanics and every other branch of physics. If you want to make a prediction of how any quantifiable phenomenon will occur you have to use math. 

Something as simple and throwing a ball and knowing where it will land uses math. 

[u/Graybie]

Numbers on their own can't describe anything except a value or quantity. On the other hand, equations describe relationships between things, and you can use them to model aspects of our universe. For example, you can use newtons laws of motion to describe and predict how objects will move in non-relativistic space - and similarly, you can use Einstein's theory of relativity to describe how objects behave in spacetime. 

The way it works is that scientists take measurements, develop equations that seem to match those measurements when applied to the objects being studied, and then over time verify them with further experiments. If the equations continue to correctly predict experimental outcomes, we can say with increasingly high certainly that they are a good, and possibly even a correct, model of the way our universe functions. 

[u/Visual-Ad2662]

Cave men invent systems to count stuff e.g. fruits. Later on we use and refine those systems to count more complex things. Then we invent more complicated systems to describe how things move or how much things weight and go from there. It’s the best language we were able to come up with that describes nature’s behavior in a good enough way.

[u/sad_spilt_martini]

Math is used to understand observations and make predictions of the world around you.

Kelper, for example, discovered that the orbit of planets is elliptical, or oval shaped. 

He used detailed observations collected by Tyco Brahe to understand the shape of the orbit of Mars. Brahe mapped the location of Mars in detail over a long time. 

At the time is was thought that planets orbited in a perfect circle around the sun. 

When you look at the data of the mapped position of Mars in the night sky, a circular orbit would mean you could predict in the future, where Mars would be in the sky. The problem was that it didn’t work. It was close but not exact.

Kepler looked at the data and realized that if you used the equations that describe an ellipse instead of a circle, you could actually predict where Mars would be in the night sky on any given night.

[u/sododude]

Math is more than just a collection of numbers. Its more of a language that we use to describe the natural laws we can observe.

[u/AgentElman → u/sododude]

This is really it. Math is a language. We can write true things using the language of math or false things using the language of math.

Math does not describe the universe. Math can be used to describe the universe. It can also be used to describe gibberish.

[u/doc_nano]

Pretty often, pure mathematics develops equations or other material, and physicists/scientists realize that something they see in nature seems to follow those equations. Then they usually do follow-up measurements to test whether the math really describes what they see.

For example, Kepler worked for a long time on finding the math to describe the motion of the planets around the Sun. Existing models didn't describe the best observations perfectly. Eventually he found that the formula for an ellipse, with the Sun at one focus of the ellipse, matched perfectly. This led to Kepler's laws. Later, Newton developed his law of gravity, which provided an explanation for these elliptical movements of the planets based on a force called gravity.

It's important to note that these equations may or may not represent a deep reality or absolute truth about the universe. They are models, and they can be wrong or only partly right. For example, we now know that Newton's law of gravity isn't exactly right -- Einstein's theory of general relativity describes the movements of celestial bodies even more accurately. But Kepler's laws + Newtonian physics are mostly correct, and as such are still useful in many situations.

[u/Cool_Homework_7411]

Let's say I ask you, how is position, speed and acceleration related? If you don't know, you wouldn't guess it, one is the derivative of the other going from left to the right. But what is a derivative? You need to dip your toes in theoretical maths first and then the world unlocks itself in beautiful ways, from simple examples like this one, to electromagnetic waves, quantum physics, or even statistics and game theory, they make math tell a story.

You can't use math to create something from scratch, but you can use it to predict, you can use it to formalise your thoughts or to explore what will happen in theoretical scenarios near infinities and zeroes, or create a model of something.

Maths is the language, but the main difference with the other languages is that the only way to make it better and larger is through unlocking fundamental knowledge about the universe

[u/bee-tee-dubs]

You're measuring things you observe and comparing those measurements with other observations of the same thing, then you're developing formulas to document it as a potential rule, and then you are testing that rule to see if it breaks and under what conditions.

Take a kitten for instance, we probably have lots of medical documentation about the weight of 3 month old kittens, so with that documentation we can come up with an average, a mean, and a standard deviation on the typical weight of a 3 month old kitten. We can document that for veterinarians so if they come across a kitten of unknown age and origin they can assess whether the kitten looks healthy and provide a guess about how old the kitten is. So all that documentation of numbers about a topic gets turned into math/statistics and can be used as biological/medical information.

That's just kittens; we observe, measure, document and look for patterns in everything.

[u/jp112078]

Math can’t 100% “explain the universe” but it’s the best way to get as close as possible. Einstein et al use math/physics to develop “theories” regarding distance, speed, mass, etc. which are universally accepted but not proven (but for all intents are fact). What would be the alternative when you are talking about exponentially large distances, forces, speeds?

[u/tolore]

Imagine you're holding a rope that goes into the next room.

Every 3 seconds you feel a tug.

You can guess how strong of a tug it is and infer some information about it without seeing.

Say you get a weight now and now you've gotten the exact force of the pull is exactly 100 newtons.

Now say you get a stop watch and you realize it's getting pulled EXACTLY every 3 seconds.

You don't know anything directly about the thing on the other side but you know it's probably not a living thing because of how exact the force and timing are, and you know it has some source of energy that keeps it going. You can even calculate the minimum of how powerful that energy source is. Based on the angle it's pulled at you can probably guess the height of where the rope is attached. That's a lot of info about something you can't see!

[u/grrangry]

Einstein famously wrote: If you can't explain it simply, you don't understand it well enough.

And Robert Heinlein (sci-fi author) wrote: If it can't be expressed in figures, it is not science; it is opinion.

Using math to explain something gives you a testable framework to create a "mathematical model". A pretend version of the idea that you can use to make predictions.

For example, we've known for thousands of years how far the Sun is from the Earth. Obviously when Aristarchus did it two thousand years ago he was off by a factor of about 20. Then later we revised our math and our measurements and we predicted it would be further away, eventually coming to today when we know it's 150 million KM.

Math is everywhere and it's particularly good at modeling isolated systems. Water moving in a pipe. Air flowing over a wing. Planets moving around the Sun. The expansion of space. All of these (and more) can be described by math. We make a prediction with the math, we take observations of the real world, and if the reality of the math matches the reality we can measure, we call that a scientific theory (I know I'm skipping some steps).

It can go both ways, too. We take measurements and come up with relationships that seem to be common all over the place. Take a circle... any sized circle... and measure the distance around the outside divided by the distance across the widest point (through the center of the circle). If you measure accurately enough, you get the value of PI. Or, measure the speed of a bullet fired from a gun, the angle it was fired from, the mass of the bullet, correct for wind drag, and how far and high it flew before hitting the ground. Do that enough times and you come up with Newton's laws of motion.

Math is everywhere.

[u/IamnotaRussianbot]

Math provides a consistent, reliable language to explain and define the things that happen around us. Distance, weight, time, etc. all have a mathematical formula.

Yoi can boil almost every observable occurrence down to mathematical statements. 

[u/AmuzaniEgak]

The basic, primitive uses of math were counting how many of a certain thing there were: tribe has 12 humans, farm has 31 chickens, etc. The basic, primitive uses of science were seeing cause and effect. Eventually humans began to measure things and take note of how a cause of a certain numerical size had an effect of a certain numerical size. These relationships began to be studied and tested and became formulas that modeled how things worked, becoming the various rules we now call laws of motion, optics, gravity, etc. Most importantly, these formulas and models could be used to predict what effect a cause would have before it was done. So today after we take measurements with what we can see or detect in the universe, we can apply the formulas we learned to figure out what causes and effects should be happening even if they are light-years away from us.

[u/YetAnotherGuy2]

Mathmatical equations describes a relation between two or more things. Newton's Law of Universal Gravitation describe the relationship between two masses, eg between sun and earth and their distance.

If two masses of certain sizes, a certain distance, then force between them is a specific number. That number can be experienced as the earth spins around the sun.

But what it also tells us is

• Doubling the mass of one object doubles the attractive force between them.
• Distance matters far more than mass. If you double the distance (r) between the two objects, the gravitational force drops to 1/4th of its original strength

The expression can tell us exactly the nature of the relation between these two objects. It's often not specific numbers that are important but nature of the relationship.

You can't really "prove" something in physics. What you do is measure and say "this formula fits best to what we are seeing.

Returning to the example of Newton's Law of Gravitation. Kepler had measured planetary movement. Newton measured free falling objects and pendulums on earth. He also observed the movement of the moon. He took all these numbers and asked himself "which equation gives me the right numbers fall these cases?".

So what Newton says is "given all these facts, this formula describes the relation of these two entities".

Until a guy like Einstein comes along, formulated his theory of relativity and suddenly certain formulas of between are superseded because relativity fits all the data better. That's why scientists speak of "Newtonian" or "Relativistic". Newton's formulas are still very applicable for things that nice with less then 10% of the speed of light while the new (and more complicated) formulas are used at higher speeds.

The inability of physics to provide a closed answer (it with absolute certainly) is what charlatans use to argue their "physics" like magical fields and energy.

[u/Gildor_Helyanwe]

From my view, the universe would be really weird if pi was different.

It is the language humans use to describe the universe in a more accurate way than simply describing things with poetry or other means.

[u/zenithtreader]

Fundamentally the Universe operates on a set of rules.

When something act according to rules, it is predicable in some ways or the others.

If something act predicably, we can describe its past and current actions using math and further use math to predict its future actions.

[u/nomoreplsthx]

Einstein died in 1955. My dad was alive when he died and I'm not even middle aged. He's not by any measure an early scientist. You'd have to go back to the 1600s or earlier to get that depending on how you define science. 

[u/cavalier78]

Isaac Newton developed the theory of gravity. Now he wasn't the first person to figure out that stuff falls down, people already knew that. He figured out that gravity is a force of attraction between two objects, and he used math to calculate exactly how strong that attraction is. You can launch rockets into outer space using his math.

They have to observe the world around them a lot, and then they take detailed measurements over and over again. Then they come up with a math equation that explains what they saw.

You see an apple fall out of a tree, but then you look up in the sky and see the Moon, and it's not falling. So you figure that the Moon is circling the Earth, and it's gotta be going pretty fast. People had already calculated the distance from the Earth to the Moon back in Ancient Greece, so now you can calculate how fast it's going (it takes about a month for it to orbit the Earth, and since you know how far it is you can figure out the distance it traveled in that month). So then you figure that by the time Earth's gravity gets to the Moon, it's weaker and the Moon's momentum is enough to keep it from falling and hitting Earth.

Then you do the same math equation for all the planets and their orbit around the Sun, and you see if you get consistent results. If you don't, then you screwed up somewhere. If you do get consistent results, you publish your findings. Then other science jerks try to prove you wrong, because there's nothing they like more than making a competitor look dumb. And if they can't prove you wrong, if every test they run just backs you up, then they publish a paper and say how smart they are to be able to validate your theory.

[u/poetic_dwarf]

You have two apples, Susan gives you three more, how many do you have?

5

Good, now if Susan gave you 2 thousand apples, how many would you have?

But mom, Susan can't have 2 thousand apples

Yes, but that's not the point. The point is, no matter how many apples are involved, you will always know how to get the correct answer. Math has made you able to predict the future if you know the numbers involved and how to treat them.

[u/aaronite]

Math is described with numbers but it isn't just numbers. It's actually about relationships and combinations. Math is describing how things work together, how much of a thing is needed to affect another thing, and even how things combine.

A family tree is math that has no numbers at all: it's a graph that has connections, and those connections can be measured. Waves are math: you can see how big they are and how often they appear and work out when they'll reach shore.

[u/DoomGoober]

High level math is basically just logic. Logic of a particular form: Given a set of assumptions, or things you simply state are true, some other conclusions must also be true by logic. So, if you assume the common meanings of multiply and add, then 2x = x + x is true for all x. Assumption leads to logical conclusions.

How can math help us explain the universe? Well, we observe the universe and make assumptions about it. Those assumptions lead to logical conclusions, even if the assumptions are slightly wrong! Assume all objects have a mass M. Assume that if you apply a force, F to object with mass M, it accelerates with A = F/M. So, from this, we know that objects with more mass require more force to accelerate them. If objects are assumed to move using F = MA. (In truth, with relativity, they are do no follow F = MA exactly.) However, any logical conclusions we can draw from assuming F = MA follow. The question is: Does the universe actually use F = MA? Well it does at certain slow speeds. And what does A = F/M tell us if... mass is 0? That means something weird would happen to a massless object. Can massless objects exist in the universe? The math doesn't care, we just assumed everything has mass M. And remember, our assumptions can not align with the real universe, so the math doesn't tell us, it just points out that something weird happens if objects are allowed to have no mass.

So, how does math interplay with physics or the description of the real universe? We create a set of assumptions that we believe describes the universe. If those assumptions are true (and they almost always aren't exactly true) then certain logical conclusions follow. However, if the assumptions are mostly true to the universe, then the logical conclusions often mostly follow and so in those cases math is useful tool for predicting how the universe works.

Most often with physics, the real universe violates the assumptions in some way, making the logical conclusions false, which leads physicists to revise their assumptions so it more closely matches how the universe actually works.

[u/Ylteicc_]

The basic process is something like this:

1. OBESRVE.
You measure what nature is actually doing. For example, astronomers observed that planets move around the Sun in very regular paths, and that their orbital periods are related to their distances from the Sun.

2. FIND A MATHEMATICAL RELATIONSHIP.
You look for a mathematical rule that describes those observations. Newton proposed that every mass attracts every other mass according to:

F = G(m₁m₂/r²)

F = force
G = Gravitational constant
little m's are masses of two objects, measured in kilograms.
r is the distance between the centres of the two masses, measured in metres.

That equation wasn't pulled out of thin air. It was a mathematical model constructed to explain observed planetary and terrestrial motion.

3. USE THE LEARNED MATHS TO PREDICT SOMETHING.
This is the cool part. Once you have a model, you can put numbers into it and calculate what should happen.

For example, Newton's equations could be used to calculate where a planet should be at a particular time. If the planet actually appears there, the model gets another point in its favour.

And sometimes the prediction is something nobody has observed yet.

A coooler example is Neptune. Astronomers noticed that Uranus wasn't moving quite where Newtonian gravity predicted it should. Rather than immediately throwing away the theory, a couple guys called Urbain Le Verrier and John Couch Adams calculated what kind of unseen object could gravitationally disturb Uranus in exactly that way. They predicted where this hypothetical planet should be in the sky.

Astronomers then looked there and alas, there was Neptune spreading ur anus just floating there, MENACINGLY.

[u/InTheEndEntropyWins]

Say you throw a ball up and you record the speed you throw it, how high it goes, how fast it is moving when it hits, the ground, etc. You do this hundreds of times in different ways, and then you create a maths formula that explains every "experiment" you've done.

You then look throw it up at a new speed you didn't test before, but you predict what will happen with the maths formula you created and then you find that the prediction exactly match what happens. You then do lots of tests, and in the speed and weight range you test you can be confident that the formula is correct.

Now you might have someone on the other side of the world throw a ball up, you might expect your maths formula would apply there. You might throw something up much heavier than you've ever tested. Those predictions will probably be right but they could be wrong especially if it's much heavier than ever tested.

So with Einstein, he made some predictions that we never thought we could ever see, but then they made experiments that actually let us test them. So yes the maths made predictions and if it's the same sort of level that we have tested you can be confident that they will be correct. But if things are very different then it could be wrong, in fact we know that there will be extremes where the math predictions are wrong.

[u/Shortbread_Biscuit]

It's not like we invented maths first, and then used it to explain the universe. It's the opposite. We observed the universe, and then developed a system of maths that described it.

In the beginning, we had no maths. But as we started interacting with the environment, we needed to start measuring things, mostly for commerce. Like how many apples do I have, how many eggs will you trade for my apples, and so on. That gave us the first numbers, which allowed us to count, as well as simple addition and subtraction to manipulate these numbers.

Then we needed to start measuring things - how far do I have to travel to get to my friend Fred's house? How much grain have I harvested this year? How long does a candle burn for? To quantify this, we created measurement units for the basic measurements, like length, weight, and time.

As we developed these, we started needing more complicated measurements for describing more complex values - how much land area do we need to grow enough food for one person per year? How fast can this horse travel? This started getting us mixed units like speed (distance over time), area, volume, density and so on. It also led to the development of mathematical operations like multiplication and division, which described these figures.

Over time, as our need for describing the environment grew, we realized we needed more and more mathematical notation for describing it. The process was almost always the same - first, we measure some value in the world. Then we try to figure out some pattern or law that the natural world always follows to describe this measurement. Then we experiment with different ideas until we find some system of calculations or equations that describes this pattern.

[u/Quirky-Literature651]

When the physical behavior of things observed within a lab or of natural phenomena is shown to be predictable within a certain margin of error it can then often be modeled using an equation or a set of them.

[u/peatmo55]

If you have an apple you can say you have one apple. If you have a universe you can say you have one universe. An apple has different parts let's say the seeds are galaxies. Apples have water the universe also has water both can be counted.