# Is mass a number?

You tell me. Can you put "transparency" in a bottle on its own? Can you put "shape" and "size" into their own separate bottles?

Why is this so hard for you? I've asked you many times, yet you can't even seem to bring yourself to attempt an answer
This is a ridiculous discussion, I suppose. You're accusing me of not bringing myself to attempt an answer to your question.

You say mass is a number. It's something we invent to explain why we can weight things close to the earth's surface. Or why that sense of weight disappears when in free-fall. What acceleration is, and so on.

Notice I use the word weight, not weigh. We use the first term for standard-mass objects, like a kg. But these are made of matter you say, not mass because mass is a number.
So it dissolves to the semantic plane, what does mass mean or what does a number mean. Or what does red mean, or a solid ball of matter mean?
What does rotation about a centre of mass mean. What could the centre of a number mean?

I mention that a transparent glass bottle isn't in my head, like invented mass, it's "in" the bottle in exactly the same physical sense the glass is in the bottle. The qualities and quantities of the bottle are in the bottle, however or if ever, I perceive and interpret them.

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When I put the ball on the scales, I'll see a number like "0.345 kg" on the display. That number is the mass of the ball. It's right there on the display! Then - miracle of miracles - it goes into my eyes and before you can say Bob's your Father's Brother it is in my head! The number "0.345", right alongside the units "kilogram".

You MEASURED the ball's mass. You compared it to another massive object, and since they were both equal, you assigned the same number and unit to the ball.

Do you not understand that you are MEASURING its mass. The ball has mass, and you are MEASURING that mass.

A stick has length, and you measure its length.
A stick has mass, and you measure its mass.

A stick has a length and mass whether you measure it or not. When you measure it all you are doing is comparing it to a different object.

When two balls are placed on a balance scale and they have the same mass, the scale will balance. You measured one ball against another and the mass was the same for both. NO NUMBERS or units. The balls simply have the same mass. They actually have mass, you can feel it when you try to throw it. Try throwing a more massive object like a shotput and you can REALLY feel it! The shotput is more massive, whether you measure it or not!

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Then you should be able to extract it, put it in a bottle and photograph it. Right?

Where can I get a bottle full of radius?
James can you please explain why it is that I should be able to do that? What is it you're doing there?
I can take a photograph of a transparent glass object and say, I have a bottle with a bottle in it, if you're prepared to accept an image is a bottle of some kind, a container say.

I say the object is the container, inside it are the mass (because of all the atoms), the centre of mass which need not lie inside, as in a torus or ring, but these are properties of the object, not my mind.

To put mass in a bottle, make the bottle out of a material substance, it brings the mass along with it.
To say that means you can photograph it, take it out and put it in another bottle is based on your questions, not mine. You haven't gotten past this.

But let's open a bottle of distances, and pour them onto the plane. I hear 2011 was a good year.

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When you put a ball in a bottle you are in fact putting mass in a bottle.

Put more people in your car and the car will accelerate at a lesser rate, because there is more mass in the car.

The car doesn't accelerate at a lower rate because there are more numbers and units in the car, it accelerates at a lesser rate because there is MORE MASS in the car.

Nobody would say "red is an object", I hope.
?? Why not? It's a property of human color perception. The perception is an object as much as a neuron is.

arfa brane:

This is a ridiculous discussion, I suppose.
Fairly ridiculous, yes. Especially ridiculous that it has gone on for this long.
You're accusing me of not bringing myself to attempt an answer to your question.
Up until now, yes. It's good that you've finally started to think it through.
You say mass is a number. It's something we invent to explain why we can weight things close to the earth's surface. Or why that sense of weight disappears when in free-fall. What acceleration is, and so on.
Yes. All of that. Mass is a concept. A concept that is quantified using numbers; hence my statement that "mass is a number".

Mass also has some units, as you pointed out previously, but the units are also conceptual.

I'm willing to concede, to be fair, that mass is not "just" a number. I concede that it is a number with some units. Does that make you happier?

Our original discussion was about energy, which I also claimed was "just a number". I also concede that energy has some units (or dimensions), although I emphasise that this was never something that I disputed.

Will you now, in turn, concede that energy is a concept, rather than being a "substance" that moves around, exists inside objects etc.? Or can you not bring yourself to concede that (or, perhaps, anything)?
.... standard-mass objects, like a kg. But these are made of matter you say, not mass because mass is a number.
Yes.
So it dissolves to the semantic plane, what does mass mean or what does a number mean. Or what does red mean, or a solid ball of matter mean?
What does rotation about a centre of mass mean. What could the centre of a number mean?
Re: dissolving to the semantic plane: yes, something like that.

Centre of mass, by the way, is just an imaginary or mathematical point somewhere in space. The centre of mass of an object, as you are no doubt aware, need not be inside the object at all. It can be outside in "free space". But we can't see it or bottle it. We can only imagine it. Do you agree?
I mention that a transparent glass bottle isn't in my head, like invented mass, it's "in" the bottle in exactly the same physical sense the glass is in the bottle. The qualities and quantities of the bottle are in the bottle, however or if ever, I perceive and interpret them.
Not true, I'm afraid.

Is the glass bottle "transparent" to UV light? If not, then "transparency" is not an absolute thing about the bottle. It is a feature of who is looking at it and how they are looking at it. It's also bound up with how they perceive it.

There is another question here: that of objectivity vs subjectivity. It is objectively true - objective meaning that all sensible people can agree - that a glass bottle is transparent to visible light. The same thing goes for mass. Everybody can agree that 1 litre of water has a mass of 1 kg under some "normal" set of conditions. Ideas like "transparency" and "mass" are useful precisely because they are largely objective rather than subjective.

Energy is also an objectively measurable quantity. But that doesn't mean it is like the "stuff" that makes up a bottle. There's no such thing as "pure energy". We can't bottle it. We can't see it. We can't detect it. All we can do is calculate it. Which makes it a number (okay, with some units).

Have we reached an agreement, or at least an impasse? Or do you want to go around the merry-go-round a few more times?

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Ghost:

You MEASURED the ball's mass. You compared it to another massive object, and since they were both equal, you assigned the same number and unit to the ball.
Yes.
Do you not understand that you are MEASURING its mass. The ball has mass, and you are MEASURING that mass.
When you say that a ball "has" mass, what are you actually saying?

Can you show me a bottle containing the mass of the ball, without the ball? If you can't show me "mass", then in what sense can you say that the ball "has mass"?

The only way you can say that is to do it the same way I do it. When I say "the ball has mass", I mean that I can associate a certain number (with units) with that ball, and that number is what I call "the ball's mass".
A stick has length, and you measure its length.
A stick has mass, and you measure its mass.

A stick has a length and mass whether you measure it or not. When you measure it all you are doing is comparing it to a different object.
This discussion is turning into "If a tree falls in a forest, does it make a sound?"

How do you know a stick has length whether you measure it or not? If you're looking at the stick, you're judging how long it is. If you want to be more accurate about its length, you're going to need a ruler of some sort.

If, on the other hand, you're not looking at the stick, how do you know anything about it?

I get it that sticks don't tend to change length when you're not looking, which is a useful feature of sticks. But that just tells us that this "length" measurement thing has some kind of objective existence, which only means that people can generally agree on what the length of a stick is, if they have an appropriate ruler.
When two balls are placed on a balance scale and they have the same mass, the scale will balance.
Yes. But that's not a feature of the "mass" number we assign to them. One ball has a mass of 1 kg. The other hand a mass* of 2.2 lb. They balance! Oh, but that's because 1 kg and 2.2 lb are the same mass, you say. What happened, then? Did some "kilogram stuff" turn into some "pound stuff"? Or did we just do a unit conversion in our heads?
You measured one ball against another and the mass was the same for both. NO NUMBERS or units.
If you didn't use numbers then you didn't measure the mass! All you did was to determine that whatever masses the two balls eventually turn out to be assigned, they must be the same.
They actually have mass, you can feel it when you try to throw it. Try throwing a more massive object like a shotput and you can REALLY feel it! The shotput is more massive, whether you measure it or not!
You can't feel mass any more than you can bottle it.

When you throw a ball, you only feel some atoms in the ball pushing against some atoms in your hand (and, before you start again, yes, we could associate a number called "force" to that push). The shotput pushes against your hand harder than the tennis ball. One reason is that there's more "stuff" (NOT mass!) in the shotput.
When you put a ball in a bottle you are in fact putting mass in a bottle.
Only in your imagination. You're so used to imagining things that way that you're having a hard time recognising your imaginary idea for what it actually is.
Put more people in your car and the car will accelerate at a lesser rate, because there is more mass in the car.
No. Because there are more people in the car.
The car doesn't accelerate at a lower rate because there are more numbers and units in the car, it accelerates at a lesser rate because there is MORE MASS in the car.
So close, yet so far.

----
* the pound is not actually a measure of mass, but of weight, but I'll skip over that here.

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Now consider a 1 kg ball.

Are you going to say that "1 kg is an object"? Are you going to say that "1 kg" is inherent in the ball? Are you going to say there's some sort of "essence of mass" in the ball? If so, can you separate out the "1 kg" from the ball and bottle it, so we can just see the "1 kg" in its own bottle?

This is essentially what arfa brane is asking us to do.
Ok, I can also consider the effort I'll need to make lifting one or both of a pair of 4kg exercise weights, I can ponder what their ponderable substance is, and whether I can bottle it when it already is.
Of course the "essence" of the ball's mass is in the ball; it's in the atoms inside the ball. The atoms in the ball aren't in my head, they're in the ball. I have to assume mass isn't a number in my head.

Centre of mass, by the way, is just an imaginary or mathematical point somewhere in space. The centre of mass of an object, as you are no doubt aware, need not be inside the object at all. It can be outside in "free space". But we can't see it or bottle it. We can only imagine it. Do you agree?
No I don't agree.

The COM of a torus or ring lies at the geometric centre in free space, as you say. It can rotate around the centre. Is is there? Is it already fixed by the geoemetry? Yes, and yes.
In the same sense that atoms are, or that the acceleration g is already around.

You don't imagine gravity and the constant acceleration; you don't imagine mass.
You can't put the spring-ness in a spring somewhere other than the spring it's in.
Hang the spring vertically, it measures it's own weight by extending a little.

Attach another weight to the end and you see more extension. This observation is in your head, but the spring and the weight are in themselves. So apart from what you see and the distances along the vertical, what has to be real, or physical? Apart, that is, from stuff that already is?

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All I'm seeing here is continued objection from James to any claim I make about anything physical, like the radius of a disk of rigid material.

He immediately wants to know if I can take this radius out of the disk, and bottle it. Why ask that? What kind of question is that?

When you say that a ball "has" mass, what are you actually saying?

I am saying the ball has a specific amount of stuff we call mass. Just like you can claim the ball is matter, I claim the ball is mass. I can even measure the mass, where you appear to not be able to measure the matter. I can quantify my claim that the ball has mass by measuring how much mass it has. Can you measure the matter that you claim the ball has?

Can you show me a bottle containing the mass of the ball, without the ball? If you can't show me "mass", then in what sense can you say that the ball "has mass"?

Objects have mass, like they have volume. Objects have different densities, which is mass per volume. Are you claiming that an object doesn't have a density, or volume? Are you now claiming that density is a fairytale, that a balloon is the same as a bowling ball? mass per volume is what objects are. A ball is an object comprised of mass and volume.

The only way you can say that is to do it the same way I do it. When I say "the ball has mass", I mean that I can associate a certain number (with units) with that ball, and that number is what I call "the ball's mass".

That number is the number you assign to the ball because it has the same mass as another object that you have standardized as that number for the same mass. There is a difference between an object having mass and measuring an object's mass. I am claiming you are actually measuring mass and then saying there is no mass, just a number. That's like saying you measured the length of a stick to be 1 meter, but length is just a number. Sticks have length, some short and some long. No numbers required, just place them side by side and find out which is longer and which is shorter.

This discussion is turning into "If a tree falls in a forest, does it make a sound?"

Trees have mass too. The problem is you claiming that a tree doesn't have mass, and then claiming you can measure the tree's mass. Outrageous!

How do you know a stick has length whether you measure it or not? If you're looking at the stick, you're judging how long it is. If you want to be more accurate about its length, you're going to need a ruler of some sort.

Some sticks are longer than other sticks. It has more length. You can measure the sticks and assign numbers to the lengths, but that is just measuring, and does not mean that sticks don't have length, that length is just a number. Outrageous!

If, on the other hand, you're not looking at the stick, how do you know anything about it?

Who cares if you look or not, a stick has a length by the pure fact that it is a 3 dimensional object in space. If it exists it exists with 3 dimensions, x, y, and z!

I get it that sticks don't tend to change length when you're not looking, which is a useful feature of sticks. But that just tells us that this "length" measurement thing has some kind of objective existence, which only means that people can generally agree on what the length of a stick is, if they have an appropriate ruler.

Sticks have length, period. If you want to measure the length then you need a measuring system with numbers and units. But sticks have length, with or without a measuring system. If humans never existed on Earth, trees would still have sticks that have length, extending out. Fact! No numbers required!

Yes. But that's not a feature of the "mass" number we assign to them. One ball has a mass of 1 kg. The other hand a mass* of 2.2 lb. They balance! Oh, but that's because 1 kg and 2.2 lb are the same mass, you say. What happened, then? Did some "kilogram stuff" turn into some "pound stuff"? Or did we just do a unit conversion in our heads?

If they balance they have the same mass. Call it what you want, but the mass is the same. You want to MEASURE the mass? Invent a system of numbers and units and have at it, measure that mass!

If you didn't use numbers then you didn't measure the mass! All you did was to determine that whatever masses the two balls eventually turn out to be assigned, they must be the same.

If two balls have the same mass, then they will have the same number of units. Unless you MEASURE them inaccurately, and end up with two of the same masses with different measurements. The scale proves they have the same mass, no numbers required.

You can't feel mass any more than you can bottle it.

Mass is directly proportional to inertia, so when I throw a more massive ball I can feel a difference vs a less massive ball. I can throw a less massive ball faster. More mass means more inertia, which means more resistance to acceleration.

When you throw a ball, you only feel some atoms in the ball pushing against some atoms in your hand (and, before you start again, yes, we could associate a number called "force" to that push). The shotput pushes against your hand harder than the tennis ball. One reason is that there's more "stuff" (NOT mass!) in the shotput.

The ball does not push your hand, YOU push the ball. The ball is simply resisting your motion. The more massive the ball is the slower you can throw it, and the more force you will feel. More mass means more inertia, which means more force, given the same individual that is throwing it.

Only in your imagination. You're so used to imagining things that way that you're having a hard time recognising your imaginary idea for what it actually is.

You are confusing measuring with actual objects. Objects have mass, and yes you can measure the mass and assign a number of units to that mass. Assigning a number to an object's mass doesn't take away from the fact that the object has mass to begin with. It's what you measured, duh?

No. Because there are more people in the car.

More people does not equate to greater mass. I could put 3 small children in a car and do just fine, compared to one 400 lb dude that make my car a dog! More MASS is what kills acceleration, not necessarily more people.

So close, yet so far.

You are in Write4U territory! LOL Mixing up numbers and reality.

Ok, I can also consider the effort I'll need to make lifting one or both of a pair of 4kg exercise weights, I can ponder what their ponderable substance is, and whether I can bottle it when it already is.
Of course the "essence" of the ball's mass is in the ball; it's in the atoms inside the ball. The atoms in the ball aren't in my head, they're in the ball. I have to assume mass isn't a number in my head.

I have just invented a measurable property called "arminess", which is defined to be the total length of all arms on any specified creature or object. The unit of arminess is the Jarm (short for "James R arm", based on the current length of my right arm).

My own arminess is roughly 2 Jarms (obviously).
I saw a dog today. It's arminess was 0 Jarms.
On TV, I saw a man who had lost part of his arm in an accident. His arminess is 1.7 Jarms.
Some industrial robots have an arminess of 3 to 7 Jarms.
When I was young, my arminess was actually less than 1 Jarm for a while.
My dishwasher has an arminess of 0 Jarms, unless you count the spraying rotor as an arm, in which case it might have an arminess of, say, 1.6 Jarms.

Now, clearly I can ponder what the arminess is of any given object in the universe. Of course, the "essence" of arminess is in the objects themselves and is determined by the atoms making up the objects. The atoms aren't in my head; they're in the objects.

By your argument, I have to assume that arminess isn't a number in my head. I have a tennis ball whose arminess is 0 Jarms. The arminess of the ball must be in the ball. Where else could it be? It's a property of the ball. Even better: it's an objective property of the ball. We can all agree on the arminess of the tennis ball, without even using a measuring instrument! Even you have an objective, presumably non-zero, amount of arminess, which could be verified with appropriate measuring devices.

We don't imagine arminess. Arminess is out there in the world, waiting to be measured!

The funny thing is, though, that until a few moments ago, nothing in the world had arminess. But now everything in the world has it - even you! It was there all along; you just didn't know it!

What do you have to say about that?

Ghost:

I am saying the ball has a specific amount of stuff we call mass.
You can call the stuff "mass" if you like, but that only muddies the waters. The mass is really a number you assign to designate just how much much "stuff" you have. Pretending that mass is the same as "stuff" is a category error. Ideas/concepts are not "stuff".
Just like you can claim the ball is matter, I claim the ball is mass.
I already walked you through what calling an object "a mass" means. The fault is in your imprecise use of language, that's all.
I can even measure the mass, where you appear to not be able to measure the matter.
Measuring something means putting a number on it, doesn't it?
I can quantify my claim that the ball has mass by measuring how much mass it has.
What you're really doing is determining how much "stuff" is in the ball, then giving that a number, which you call its mass.
Can you measure the matter that you claim the ball has?
I'm not sure what you mean. A measurement needs a unit of measure. "Stuff" doesn't come with units of measure built in.
Objects have mass, like they have volume. Objects have different densities, which is mass per volume. Are you claiming that an object doesn't have a density, or volume? Are you now claiming that density is a fairytale, that a balloon is the same as a bowling ball? mass per volume is what objects are. A ball is an object comprised of mass and volume.
Well, no. A ball is made of atoms, stuff. It isn't made of mass and it certainly isn't made of volume.

Can you show me a bottle full of volume? Can you buy me a cup of mass?
That number is the number you assign to the ball because it has the same mass as another object that you have standardized as that number for the same mass. There is a difference between an object having mass and measuring an object's mass. I am claiming you are actually measuring mass and then saying there is no mass, just a number. That's like saying you measured the length of a stick to be 1 meter, but length is just a number. Sticks have length, some short and some long. No numbers required, just place them side by side and find out which is longer and which is shorter.
Sticks also have arminess, as you know. It happens to be zero Jarms. You can measure it.

Placing two things side by side, by the way, is a kind of measurement. Just a relative one. We can place two objects side by side and compare their arminess, too.

Are you going to claim that arminess is a fairytale and that a tennis ball is the same as a dog? Arminess is what objects are! Objects are comprised of arminess! Or aren't they?
Trees have mass too. The problem is you claiming that a tree doesn't have mass, and then claiming you can measure the tree's mass. Outrageous!
I've been very clear. When I say a tree "has mass", you can always take that to mean that there's a number I can assign to the tree that I like to call its mass.

So yes, the tree has mass. Its mass is a number. But its mass is not in the tree. It is in my head, or on a piece of paper, or in a computer, or wherever.
Some sticks are longer than other sticks. It has more length. You can measure the sticks and assign numbers to the lengths, but that is just measuring, and does not mean that sticks don't have length, that length is just a number. Outrageous!
You can measure the arminess of a stick and assign a number to that. So, by your argument, arminess isn't just a number. It's an inherent feature that sticks have. Right?
Who cares if you look or not, a stick has a length by the pure fact that it is a 3 dimensional object in space. If it exists it exists with 3 dimensions, x, y, and z!
How do you know there's even a stick if you don't look at it? (If a tree falls in the forest...)
Sticks have length, period.
Yes, and an arminess!
But sticks have length, with or without a measuring system. If humans never existed on Earth, trees would still have sticks that have length, extending out. Fact! No numbers required!
Would trees still have arminess, too, if humans never existed? They'd still have their little sticky arms sticking out, right? No numbers required?
Mass is directly proportional to inertia, so when I throw a more massive ball I can feel a difference vs a less massive ball. I can throw a less massive ball faster. More mass means more inertia, which means more resistance to acceleration.
Mass is a measure of inertia, or resistance to acceleration. It isn't the cause of inertia. How could a number cause something like inertia?

That's like saying that the reason I have two arms is because my arminess is 2 Jarms.
The ball does not push your hand, YOU push the ball.
Please google Newton's third law of motion. Get back to me when you've done that.
You are confusing measuring with actual objects. Objects have mass, and yes you can measure the mass and assign a number of units to that mass. Assigning a number to an object's mass doesn't take away from the fact that the object has mass to begin with. It's what you measured, duh?
The statement "objects have mass" is equivalent to "There is a number, called the mass, that can be associated with an object."

When we "measure the mass", we're doing something that will allow us to assign an objective, repeatable, numerical value to the number called "mass" for that object.

By your argument, assigning a number to arminess doesn't take away from the fact that the object has arminess to begin with. But does it, really?
More people does not equate to greater mass. I could put 3 small children in a car and do just fine, compared to one 400 lb dude that make my car a dog! More MASS is what kills acceleration, not necessarily more people.
More matter is what kills acceleration, not more mass. How could a number affect acceleration?
You are in Write4U territory! LOL Mixing up numbers and reality.
The nervous LOL is back. Ho hum.

Measuring something means putting a number on it, doesn't it?

What are you measuring?

What are you measuring?
Try to keep up!

You said you were measuring mass. Remember?

Putting two things side by side and comparing some feature of them, by the way, is a kind of measurement. It's just a relative one. For example, I can tell, without making a quantitative measurement, that I have more arminess than a tennis ball. Precise measurements can confirm that and provide more detailed information.

Please google Newton's third law of motion. Get back to me when you've done that.

If I throw a ball and accelerate it, there is a net force greater than zero. The greater the net force the greater the acceleration. Zero net force means ZERO acceleration.

The very fact that I accelerated the ball is evidence to the fact that the net force was greater than zero. So the ball did not "push back" with the same force as I pushed it. The net is the difference.

Sorry, Newton was wrong, and I proved that decades ago!

Try to keep up!

You said you were measuring mass. Remember?

Measuring mass? Measuring a number?

I have just invented a measurable property called "arminess", which is defined to be the total length of all arms on any specified creature or object. The unit of arminess is the Jarm (short for "James R arm", based on the current length of my right arm).
I've thought about it, and all I can say is, if you invented a measurable property that is based on the length of your right arm, then you didn't invent the length of your right arm, you just decided it's a unit of length.

So what? I can choose arbitrary names for pre-existing physical properties too.
We don't imagine arminess. Arminess is out there in the world, waiting to be measured!

The funny thing is, though, that until a few moments ago, nothing in the world had arminess. But now everything in the world has it - even you! It was there all along;
Yes, any change of terminology for a physical thing like length or time, doesn't change the fact it was there before you change the name, and after!
But it doesn't explain how mass is a number. I don't think you've managed that one yet

Mass is a measure of inertia, or resistance to acceleration. It isn't the cause of inertia. How could a number cause something like inertia?
A density of matter with mass m, at a distance R from an axis of rotation, even when it isn't rotating and has no angular momentum, has a moment of inertia. If there is no cause needed for actual rotation, what "causes" the existence of R and the inertia tensor? Is that why it's a scalar (0,2) object?

R exists and is fixed for a solid object, so consider the sum of individual small volumes of a ring of solid material. A solid torus, topologically. The inertial moment for a 2-torus with total mass M is \$\$ I = MK^2\$\$ where K is the radius of gyration--where all the mass could be concentrated and not alter \$\$ I\$\$.

For a torus K = R.

Mathematically speaking there is no difference between summing over volumes and summing over individual mass densities to get \$\$ I\$\$. It works for the same reason a solid ball has a centre of mass. If you replace the ball with a smaller, denser one with the same mass it has the same inertial mass.

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More of the thinking I've done about the "mass is a number" argument James is determined to keep using.

After admitting that it has units. So it's not a number, it's a number of units. It's a number "with" units if that's what you mean to say.

Physics however, will be brutal about it. James wants to answer the question: when did mass first appear in the universe? So he can answer the one about what humans measure, or how they measure it, or what they call a unit of length.

Perhaps, along the way we can answer the one about when did a meaningful distance first appear?

/puff_puff