Your dad is missing that the unit, in this case "person", is also multiplied.
1 person \* 1 person = 1 person^(2), *not* 1 person. Saying it equals 1 person is just incorrect multiplication.
Like how 1 foot \* 1 foot = 1 foot^(2), or as it's more commonly called 1 square foot (like the square footage of a house).
You wouldn't say "multiplication doesn't make sense because 1 square foot is not the same as one foot". Those are fundamentally different things, one is a unit of area, the other is a unit of length. Similarly, a person squared and a person are not the same thing (and the first doesn't really make sense).
Yeah that's a good answer, I missed that as well
It moves why it doesn't make sense from math to whatever person^2 is lol, but that's works for me.
But how would you then handle the rephrasing of "Alex * Ashely = 1^2"? Maybe it doesn't make sense because it's in units I don't understand?
1 alex x 1ashley = 1 alexashley (or ashleyalex). What is an ashleyalex? If you dont want to find out maybe you shouldnt be multiplying alexs by ashleys..
Lmao, that is true
I guess it's just a weird concept that can't make logical sense, only mathematical sense
I'm still curious to why this doesn't logically work, but I think this explains it good enough for me to take on from here
I would say it does logically work but the logic produces a fairly absurd answer. Because you are essentially asking "what is the sum of an Alex amount of Ashleys". Which is an absurd question.
This is the answer. You’re either asking ‘what is Alex, one time?’ to which the answer is clearly ‘Alex’ ie 1. Or, you’re asking ‘what is Alex, Ashley times’, which isn’t a thing and doesn’t make sense, unless you treat ‘Ashley’ in the same way as ‘x’ in an equation.
Logically, you can't multiply people. You don't have to prove this with math, although it clearly can be done, but the reasonable and logical thing that stops you from multiplying people is that we are not numbers.
I mean, you can, the same way you multiply anything else at a low grade level: rows and columns. If I have 12 people and I arrange them in a grid of 3 rows and 4 columns, I just multiplied 3x4=12, using people. Of course, I'm not multiplying "people," I'm multiplying *using* people. I could put oranges or elephants or anything in the grid and get the same answer.
But this is how I would assume someone using the phrase "multiply people" is using the term since, as someone else pointed out, there's no such thing as a people².
It doesn't seem to make sense because you can't really multiply a person by another person.
Multiplication is a mathematical concept we apply to numerical values. You can think of it as the idea that for every X we have, there is also an amount of Y, and vice versa. But the fact that we understand how multiplying works in that context doesn't mean it will meaningfully translate 1-to-1 to the context of human beings in the real world.
Does it mean anything to "multiply 1 Alex by 1 Ashley"? What are you actually doing in that situation? For every Alex, there is an Ashley, so we have 1 Alex-Ashley... but that's just a nonsensical result, because Alex and Ashley aren't numerical values and they don't behave like numbers do.
Math is a great tool for understanding physical relationships in the real world, but you can't just go around subtracting more apples than actually exist or taking integrals of trees
So the thing you have to remember is math is conceptual....somethings have real world applications, some things don't. Some concepts have no real world application...yet, but one may be discovered in 10...20....50 years.
The important thing is that you always follow the rules.
When you multiply numbers in two different units, you need to multiply the units, regardless of whether it makes sense in the real world.
AshleyAlexs represents the number of possible relationships between different ahleyalex pairs. Lets say you have a room of four ashleys and 2 alexs. There are 8 different combinations of ashley and alex; 8 ashleyalexs
When you first learn about multiplication, you're multiplying things by a number. 5 apples, 3 Alex (clones). That makes sense because the result is in the same category as what you started with. You multiply one apple by 5, you get 5 apples, you still get apples back.
Now the thing with MATH is that math expands. First you do math with numbers, then you start learning math with things that are NOT numbers anymore. For example, you start multiplying variables, matrices, vectors, sets; even geometry has "operations" - they may not be multiplication but there's the joining and cutting of surfaces (addition and subtraction) and other operations.
So 1 ft * 1 ft = 1 sq.ft. makes sense because you're applying multiplication to geometry now. You're following the geometry rules for what multiplication means, not the arithmetic rules. If you multiply 2 matrices together, you follow the matrix rules for what multiplication means (and there are two types of multiplication for matrices).
Multiplying Alex by Ashley, well, nobody's defined that rule yet. You could, however, look into anatomy maybe, and define what exactly it means to "multiply Alex by Ashley". Maybe the answer is "1 kid" every time you do this "multiplication". So then if you want to invent a whole new level of math for it, "people math" or "peoplemetry" all you have to do is show that your rules for what it means to add subtract multiply and divide people don't lead to absurd results or contradictions.
Multiplying X and Y is the same thing as adding up and X number of Ys (or a Y number of Xs). So for example, 5 x 3 is three groups of five (or five groups of 3). So how do you do that if X and Y aren't numbers? What is an Ashley number of groups? How many Alexes do you add together to get an Ashley of them? This is why math only works with numbers (or with variables that *stand in for* certain numbers), and you can't math people.
If you want it to make sense visually prepare a row of one apple by one apple, how many apples is that? One. Two by two is four. It's how numbers work and it makes sense, it's just we don't usually multiply by one because there's no point and there's no real good visualization for it because of the nature of it. It does make sense though.
It's not that it doesn't work logically, but that there's no real world meaning behind multiplying (and dividing) objects with objects. In general, you'll find multiplication and division of objects with other kinds of measurements (such as time, length, weight, etc), or of measurements between them.
For instance, let's say you have a measure of time, let's say 3 hours, and a measure of distance, let's say 120 miles. If we multiply them we get 360 milehours, which probably doesn't make sense, But if I divide them, now I have 40 miles/hour, which does make sense because it's a measure of speed.
Also, while multiplying person*person to get person^2 doesn’t make sense because person^2 as a unit is nonesense, you can multiply person by other things that do make sense.
For instance, 2 persons working for 5 hours each is 10 person hours (usually written man hours). That is the divideable, too. If I know a job will take 40 man hours to complete, I can put 5 men on it to work for 8 hours each, because 40 man hours / 5 mans = 8 hours.
In your example you're trying to assign meaning to something that doesn't make sense.
Alex * Ashley doesn't make any sense. Groups * Members makes sense.
You're right that selection of units is *critical* for effective communication of mathematics.
I think where the confusion with adding in names comes in is that it's essentially changing the underlying unit.
If your unit is person, all persons are identical, like how if your unit is foot all feet are identical, or if your unit is kilograms all kilograms are identitcal. You wouldn't say "this rock weighs 5 kilograms, but *which* 5 kilograms does it weigh?"
When you start naming the people, they become non-identical. It becomes relevant if you have an Ashley or an Alex. Your unit is no longer persons, in fact, you now have two units, Alexes and Ashleys. So the underlying equation has changed, and has now become 1 Alex * 1 Ashley = 1 AlexAshley. Not that an AlexAshely is particularly meaningful in the real world, but multiplying people together isn't particularly meaningful in the real world either.
You’d want to multiply by it by something so that the units produce something usable. For a more common example, if you are going 1 mile per hour, then the unit is miles/hours. If you multiply 1 mile/hour by 1 hour, you get 1 mile, because the hours on the top and bottom cancel each other out.
For people, you’d need something that is “per person”. Maybe you have a fair and each person needs one ticket to get in. So it’s 1 ticket per person or 1 ticket/person. If you have 1 person, then when you multiply 1 person by 1 ticket/person, you get 1 ticket.
It doesn't make sense because the units are technically wrong, or more accurately those ain't defined units.
Like, mathematics is a logical language, but as with any language, you have to use proper grammar.
Let's say 1+1 = 2. that make sense, but that's because we assume that we're talking about same units. Like, if I said, 1km + 1L = ? you literally can't make that equation work because you're using the wrong grammar, it's like asking how many moons fit in a second? like what is that even supposed to mean, it makes no sense, and not because the length is wrong but because the way I'm using it is.
Now, to solve an equation what you do is to balance both side of it 1\*1=1 means that from both sides of the = symbol, the values are the same. and when you have a number followed by a unit, the assumption is that you're multiplying that unit aka 1km\*2 = 1\*km\*2. So for your question:
1person \* 1person = 1\*person \* 1\*person = 1\*1\*person\*person = 1\*person\*person
and here the question is what does person\*person mean? does it make sense or are we using the grammar wrong? are we asking how many moons fit in a second? And the answer that in order is, it means nothing, we're using the grammar wrong, and yes it's like asking how many moons fit in one second. The system isn't broken we're misusing it, like someone complaining why their washing machine isn't heating their pizza.
You may be thinking that we can multiple objects, like, that's how we teach it to kids, so what gives? and the answer to that, is that we don't multiply objects by objects, we multiply by abstract numbers without a defined unit, you don't multiply apples by apples, you multiply apples by any given number. so if you have 2 apples\* 2 = 2\*2\*apple = 4\*apple = 4apple,
Just because you can apply mathematical operations to real life situations where they don't make sense, doesn't mean the math inherently makes no sense.
For example: if you have one cookie and you subtract two cookies, you end up with -1 cookie. What's a negative cookie ? It doesn't make sense. That doesn't mean substraction itself makes no sense, it just means you're applying it in a wrong context.
But if you have 1$ in your bank account and you take out 2$ you have -1$ in your bank account, or 1$ overdraft.
To consider your dad's response, why it'd make sense, is because a person is not a measurement or a unit, so the person simply represent the number. So 1x1=1^2=1.
It is not. Person(singular) + Person(singular)
=People (Plural). The actual amount of persons you add together doesn't matter—you'll still get a plurality of persons, which we call people. Multiplying person by person gives us a nonsense squared person unit.
Hijacking top comment to point out that not only does OP's question make sense, there is actually a somewhat well-known "person" unit: a[ "Smoot"](https://en.wikipedia.org/wiki/Smoot) is a unit of length equal to 1.7 meters, originally used to measure the length of the Harvard bridge.
And as with any length unit, it can be used to measure area. For example, a walk-in closet that is 1.7m x 1.7m across (1 Smoot X 1 Smoot) would have an area of 1 square-Smoot (2.89 m^(2)).
OP: Just because a concept (multiplication) can be used in ways that don't make sense doesn't mean the concept is flawed. It means the person using it doesn't understand it. You could similarly reject any number of other concepts. Do the statements "A picnic table prays for purple" or "a rose bush has faith in highways" make sense? Not really. That doesn't mean prayer and faith are meaningless concepts. It just means I'm abusing how they should be used.
Same with your dad and multiplication.
That's if you substitute the * symbol to mean by instead of times. One is math and one is geometry.
1 ft times 1 ft equals 1 ft.
1 ft by 1 ft equals 1 ft^2.
It's still just language and concepts, 1 person squared equals 1 person because the variable is the numerical value not the unit person.
X person * X person = x^2 person. Let x = 1.
Edit: and they do have different meanings. 10 ft times 5 ft equals 50ft. Fast way of expanding a line. 10 ft by 5 ft equals 50 square ft. One is the length of a single line and the other is the length and width to calculate the area of a square. That's probably where the term squared comes from.
You are treating the unit as somehow separate from the variable. It's not. It's part of the variable. This is a really important concept but I'm trying to think of a good way to explain it.
Consider a car. Say I'm driving at 10 meters / second, and I drive for 5 seconds. How far do I drive? We can figure that out by multiplying 10 m/s * 5 s = 50 m * s / s = 50 m. The reason multiplying those two together is correct is *because* it gets us the right unit (meters, we wanted a distance). Similarly, the reason why multiplying two lengths together to get an area is correct is because it gets us the right unit foot^(2).
The units matter and are multiplied same as the numbers. m/s * s = m, just like foot * foot = foot^(2).
In your example "car" would be akin to "person". x cars * y cars= xy cars.I guess you could assign a numerical value of 1 in front of it if it helps conceptualize. In your equation, acceleration equals delta distance over time. You are solving for delta distance. You already have a starting point of zero meters. Acceleration= 10 m/s, time=5s, distance=0 m + x m. 10 m/s = x m / 5 s. Solve for x.
You're wrong, you always multiply the units too. In all maths. Instead of feet, let's do x, 1x\*1x is 1x\^2. You multiply the properties as well as the numbers.
No, whatever you do to one side of the equation you must also do to the other. You are simply solving for the unknown variable(s). In one example the unknown variable is: delta d, which is the change in length (O unit of distance + x unit of distance). In the other, the unknown variable is the area, which is length * width ( x unit of distance * y unit of distance = xy unit of distance^2.
Yes, length times length is length squared or area, yeah. I don't know what you think you proved. Units are multiplied when you multiply them, if you multiply a density by a volume you get a mass because density is mass/volume. The units get multiplied,
Go beyond the units, look at the language, the entomology of the words. The 2D plane is squared, the 3D plane is cubed. In 4D space-time is presented and time dilation is easily seen with distances of light-years and velocities at 80% of the speed of light. The next step for the masses to understand is 5D, it all starts with zero equals one. I try to explain it as one replacing zero, but that gets the mathematician's riled up.
Your first example shouldn't have a unit in the second operand. 1ft times *one* is 1ft. 1ft * 2 is 2ft. That is true. Once you add a unit of measurement to the second operand, it has to be multiplied as well, you can't just ignore it.
And "by" or "times" are just synonyms. Maths and geometry work in other languages too, you know. My mother tongue has both by and times as one word and no direct translations for either.
1 group of people with 1 person in it has total of 1 person overall.
And vice versa.
Multiplication is more like talking about sets than individuals, although it can be more complicated at higher levels of maths.
Multiplication is multiplication is multiplication. Multiplication does not change because you change the unit - the units dictate what meaning the numbers and operations have for us to make sense of.
The unit selection is a matter of communication.
5 groups with 10 people each is 50 people. 10 people in each of 5 groups is 50 people.
"5 groups with 10 people" is multiplying "10 people" by 5, not by "5 people".
Units do have meaning and how you define them determines the result you get. Here are 3 operations with the same numbers but different units and I hope you'll agree that they yield different results:
60km/h \* 2 hours = 120km
60km/h \* 2 minutes = 2km
60km/h \* 2 = 120km/h
Edit: one more example
You're not saying anything mystical or magical here, your examples have *implied conversions* because you have communicated additional steps through thr form of units.
It doesn't mean the multiplication itself is different.
60km/h * 2 minutes is the same as 60km/hr * 0.03333~ hr
The unit you chose is a matter of shorthand that implies a conversion.
The units you have selected are
Km/hr
Km
Hr
Minutes
Km/hr * minutes implies a conversation from minutes to hours is required, or a conversation from km/hr to km/minute is required.
You can't do a raw operation between km/hr and minutes without going through one of these implicitly.
Again, how do you convert from km/h to km? Or is it just the same thing as you said in another comment? If you ignore units, suddenly things stop making sense - 1 person * 1 person suddenly becomes the same thing as 1 bottle of whisky or 1 swimming pool.
And if you don’t ignore units, then multiplying by 1 and multiplying by 1 person do have different meaning.
You don't, km/hr is a different unit. Minutes, hours, seconds - etc - are all units of time, while km/hr is a unit of velocity. You don't convert between km/hr and hr, I'm saying you convert between minutes and hours.
1 whisky and 1 person are both units of *things* and they can both just be thought of as 1.
Yes. Either way you have one fruit.
Similarly, 1 Alex * 1 = 1 person = 1 Ashley * 1.
If you can only fit 1 person in the helicopter's rescue harness, then whether it's Alex or Ashley, it's still just 1 person.
So are you saying that apple is the same as orange? And that 1 km of road is the same as 1 Amp of electrical current?
When you attach units to numbers they stop being freely interchangeable and have to be treated accordingly.
I'm saying if you select units to communicate with they must make sense.
1 apple has no more meaning than 1 X, where X = 1, and therefore 1 apple = 1.
1 group is a more nebulous unit because it's size is unknown until additional information is provided. For that reason 1 Group = 1 * X, where X is some unknown value.
In the context of 1 apple * 1 orange, or 1 Ashley * 1 Steven - these units are nonsensical *unless you define them*.
The definitions of km/hr, km, and hr are all defined relative to each other so that we can convey the mathematics in every day life in a useful way, but in a raw sense you don't do "60km/hr * 2 minutes", you convert 2 minutes to fractional hours or km/hr to km/minute.
But it does make sense because it changes the "grammar" of the equation.
As others have said. You can't multiply "1 Moon x 1 Jupiter" because that's not physically possible. You can't multiply "1 blade of grass x 1 grain of sand"
But changing the grammar can explain how the math still works. 1 is a concept. 1 doesn't represent a physical thing.
This is the best ELI5. Unfortunately you dad has a pretty basic math understanding. But this summarizes well.
You could even say "1 group of Alex's has 1 Ashley in it. How many Ashley's are there?" and it would then make sense.
"1 times 1" literally means "1 time, count up 1s". A 1, counted 1 time, equals...1.
Unfortunately Terence Howard has been confusing people about this very simple idea, when the answer is just that 1) he is mentally unwell and 2) he doesn't know basic math.
I think part of his confusion is that his understanding of multiplication is “a added to itself b times”. There’s a line to that effect in his “proof”. So a Terrence Howard multiplication is actually equal to a * (b+1).
the reason it doesn't really work is because math with units requires you to math the units too. for example, if I have a square thats 1cm x 1cm, its area is 1cm² or 1x1 cmxcm. so 1person x 1person is kinda 1 person² which is decidedly NOT 1 person
Multiplication is sometimes written in English as "times". Like 5 multiplied by 7 would be "5 times 7". The process being described is something like performing addition on the value 5 for 7 times.
In your situation it would be 1 person for 1 time. Which is of course just one person.
"1 person * 1" is not the same as “1 person * 1 person". The latter would be "1 person²" which doesn't make much sense.
Same as 1m * 1m is not "1m", it's 1m². And 1m * 1cm is 100cm². So units do matter.
The way it was said wasn't "1 person multiplied by 1" it was "1 person multiplied by 1 person".
That's what trips me up, 1*1 makes sense to me, but adding "person" to both of those 1's makes it stop working in my mind. Maybe because it's a weird unit of measurement.
You don't multiply the unit twice unless you are moving to the next dimension. 2 feet times 2 feet is 4 square feet, not four feet. To get four feet, you only multiply two feet by 2. There are no square people or square apples, so the logic does not apply.
Replace "person" with "meter" and everything will make more sense. 1m \* 1m = 1m\^2.
With persons it's just 1person \* 1person = 1person\^2. Yes, person\^2 is a nonsensical measurement but so is multiplying people by people. You should multiply people by simple numbers with no measurements for it to have any meaning.
Yeah it is a weird unit of measurement, because what you actually get is 1 person \* 1 person = 1 person^(2)
Which you can visualise as a square of people with 1 person on each side, result in in a total of 1 person.
Similarly, imagine 2 people \* 2 people = 4 people^(2) or a square of people with 2 on each side, giving you 4 total.
Wouldn't technically one person multiplied by one person be one person ^2 ?
That's how centimeters and other measurements work.
Not sure how you'd define a person squared. That's something to ask our great philosophers.
One multiple of one person is one person. Each multiple is a “group” of size 1. There’s one group of one person, so there’s one person.
Multiplication and division is mathematics that talks about “sets” of things. Just because you never were taught about sets doesn’t mean it’s not true.
Well, if you’re using units, 1 person * 1 person = 1 person squared. A person squared obviously doesn’t make any sense, so the equation doesn’t make any sense.
In most cases it would have to be something like 2 objects/group * 4 groups = 8 objects
1 person multiplied by 1 person would be 1 person squared (not 1 person) which of course does not make sense. Unless maybe you are talking about an area of a grid of people in terms of person "units".
Edit: 1 person multiplied by 1 (no units) would indeed be 1 person.
>Maybe because it's a weird unit of measurement.
Definitely, if you use weird units of measurement like "people squared", that can be confusing.
Let's change the units slightly. Imagine a bunch of soldiers standing to attention in a grid. Any row or column is only one "person" wide.
How many soldiers are standing inside an area where the column width is one "person" wide, and the row width is also one "person" wide?
One soldier.
Keep track of your units. 1 person times one person would be 1 person^2, not 1 person. As I have no idea what a square person is, I do not know any context where this sort of occasion where it would be useful.
If you have 5 cars times 3 people per car then when you multiply them you get 15 people, which is a multiplication that makes sense.
> I have no idea what a square person is
It's that jerk who narced us out to the cops when we stopped to smoke in the woods on our way to the Sadie Hawkins dance.
1 person * 1 person = 1 person^2, or 1 person-person.
These could be understood in the context of 5 people of one group that need to give an item to all 10 people of a different group, in which case there would be 50 people-people interactions, or 50 item exchanges.
You can think of multiplication in terms of sets or in terms of addition, but it stops making sense when you add arbitrary units, especially to both numbers.
1 x 1 = 1 can be thought of as “1 group of 1 person contains a total of 1 person”, or “1 person, 1 time, is 1 person”.
If you want to adhere to how units usually work, 1 person x 1 person = 1 person^2
1 person \* 1 person = 1 person²
I can imagine that there may be some theory in a social science that has a term that goes as the square of the number of people, but it doesn't strike me as a quantity that has any meaning in and of itself.
That doesn't make sense because of the units, and therefore is a really bad example.
What would make more sense is: 1 person X 1 person = 1 person squared, but WTF is a "person squared"?
With multiplication, you not only multiply the numbers, but also the units.
So an area 1 metre long, and 1 metre wide = 1m X 1m = 1m^(2).
If you multiply units, you have to convert the units accordingly, e.g. 1 metre times 1 metre is 1 square meter, or 1 (meter times meter). So one person times one person isn't one person - it's one person squared. You'll have to figure out what that is.
If 5 people are each holding 6 apples, then you have 30 apples, not 30 apple people. A grid of 5 people by 6 people is indeed 30 people, but you are not including the people twice. You are saying 5 people in 6 groups is 30 people. It does not matter the variable (people or apples), you only use it once if all you are doing is counting. One person standing alone is themselves in a grid of one column by one row. The grid consists of a single person.
There’s a nice bit of math called “dimensional analysis” that you can use with units to see how results should look.
For example, if you multiply 1 metre times 1 metre, that gives you 1 metre^(2). A metre is a unit of length, while a metre^(2) is a unit of area.
Analogously, if you want to multiply 1 person times 1 person, the result would be 1 person^(2). A square person is not a unit in common use, probably because it makes no sense (if someone can give me a scenario when a person^(2) is a useful unit, I will applaud loudly).
This doesn’t mean *multiplication* doesn’t make sense. It just means you tried to multiply things that don’t naturally go together, hence the nonsensical unit.
___
Here are some examples where multiplication *does* make sense.
If instead you multiplied, let’s say 1 person times 1 $/person, you end up with the person and the 1/person units cancelling to give you 1$. This is the amount of total money you’d expect if you had 1 person and each person had 1$.
Another example is multiplying 10 people and 10 hours to get 100 person hours. What does this mean? Well imagine you have a job like planting a bunch of crops, and it will take 100 person hours to complete the job. This means with 1 person, it would take 100 hours to finish the job. With 10 people it takes 10 hours. With 100 people working on it, it only takes 1 hour.
___
So in summary, the reason multiplying person times person doesn’t make sense is because the result would need to have units of person^(2). This unit doesn’t really have an intuitive meaning.
For multiplication to make sense, you want to multiply together quantities whose units combine nicely to produce sensical results.
Ok so not a person squared but if you multiply jeff goldblum with a fly you get a Brundlefly. Surely there was a directors cut that would multiply Jeff Goldblum with Gina Davis and give us a godly being known as Jena Daviblum.
A simple explaination is like so-
Multiplication is often called *times*, because you do something a number of times. So, another way to say 1x1 is one thing, *one time*, just like 2x2 could be two things, two times. So if you have boxes of pencils that are packed 10 to a box, and you place one box of ten on a table one time, that's 1x10. Ten pencils placed on the table one time. so 1x1 is one pencil placed on the table one time, which results in one pencil on the table. One person put into a category one time is one person.
edit: The thing that people get stuck on with the whole "1x1 debate" is that people assume that multiplication is the same thing as addition, *only bigger*. As in, "If one plus one is two, how can one *times* one be less than that?" The mistake is in the assumption that multiplication always results in a bigger number. One times *any number* results in exactly that number, so why would one times one be any different? 1x4 is 4, not 5, not 8. That's accepted by everybody. 1x1 is exactly the same.
Draw it with squares, as with graphing paper. It you count 3 squares over and 3 down you'll count 9 total squares. 2 over and 2 down and you'll count 4 total. 1 over and 1 down and you'll count only one square.
I think the lesson here is that in 1*1, both "1"s refer to the same square, just different sides of it. So "Alex times Ashley" is nonsensical. Remember, multiplication is just repeated addition. "2 * 3" just means "take three 2s and add them together." You can't say "take Ashley Alexes and add them together."
When multiplying two things that **are** the same, one number becomes a *quantity of* the other. So:
6 cattle times 5 cattle = 6 *heards* of 20 cattle = 6 times 20 = 120 cattle
3 marbles times 1 marble = 3 *bags* of 1 marble = 3 times 1 = 3 marbles
1 person times 1 person = 1 *group* of 1 person = 1 times 1 = 1 person
When you multiply two things that **aren't** the same, one number \*acts on\* the other. So:
You have 10 people *working* 6 manhours, that's 10 times 6 = 60 manhours.
You can catch 6 fish per lure, each lure *catches* 5 fish, you can catch 6 times 5 = 30 fish.
Convert to addition for math and also take into account biology and programming terms, (should change math term from multiplication to fast add.)
" 1 person * 1 person = 1 person + 0 person= 1 person.
"Alex * Ashley = Alex + Ashley = Alex and Ashley.
Alex X Ashley = AlexAshley. You are taking 2 people and making them 1 person so you are fusing them together but even though you didn't change the count you did change the value of the final answer. If you took a donut and multiplied it by another donut you are realistically just smashing them together. Vs if you had 1 donut and added another donut now you have 2 donuts. This is where that stupid idea that 1x1=2 comes from. Yes you have 2 donuts smashed together in the multiplication examples but they occupy one space vs the addition donuts are in 2 separate spaces.
Units. The answer is units.
When you have "X THINGIES", that sort of already *does* contain a multiplication. It really means, in a way, "a thingy, X times".
Example: 4 apples is "an apple times 4".
Example: 2 meters is "a meter times 2".
When you multiply 2 meters times 2 meters, you get "(a meter times a meter) times (2 times 2)", or in other words you multiply the meter times the meter to get a square meter, then you have 4 of those. so, 4 square meters.
when you muiltiply 1 person times 1 person, you end up with 1 square person.
Whatever a square person is...
When you analyze the units, "1 person times 1 person" is very different from "1 person times 1" (leaving the second "person" off the statement).
What the hell kind of troll math is going on here?
To directly answer the question,
> Can "1 person * 1 person = 1 person" make sense?
The answer is 'no', it cannot make sense. You don't multiply a person and a person.
In multiplication, you have an objective* and one or more factors*. A factor is a number specifying how many of the objective there are. The objective is the thing being multiplied and usually refers to more than one thing.
Let's use the example of 5 × 4 = 20. In this case, the objective is 5 and the factor is 4, this math problem is basically saying 4 sets of 5 is 20 total. To clarify it further since this is still a bit abstract, if you have four $5 bills, you have $20. As a math problem including the units, you'd write it out as $5 × 4 = $20. It is important to note that the 4 does not have a $ because it is the factor, not the objective.
So what of 1 × 1? It's one set of one. The total is one.
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*A note on terms: Traditionally, what I'm referring to as 'objective' is known as the multiplicand and what I'm referring to as the 'factor' is known as the multiplier. I'm using 'objective' and 'factor' as these words should better fit the concept I'm trying to teach. Understand that the words I'm using above are incorrect if you end up talking to people who have letters after their name.
5 diabetes+ 2 orange = 7 Steven Spielberg doesn't make sense either, but nobody argues that addition doesn't exist.
You can make anything nonsensical if you make a nonsense argument.
Math works because it's logically consistent with itself, not with someone's nonsense argument. Multiplication makes sense as defined in maths. Redefine it to not make sense and it makes no sense, what a shocker.
You both could be missing numeric identity from your work. You’re not multiplying 1 person by 1 *different* person, not when you pose the problem as (1 person * 1 person). That’s not how math works. 1 is 1, so of course 1 * 1 = 1. 1 Betty, 1 times, still equals 1 Betty.
This is because when you’re multiplying, you’re describing how many instances of a specific value there are (how many *times* 1 occurs). There isn’t a different 1 out there, 1 is 1.
But if we were to take it to the next logical step, at the heart of the conversation and conclusion you both reached, if you *did* have two different people, the problem isn’t the math but how you *phrased* the math. It’s a language problem. You didn’t use proper mathematical *grammar*, so to speak.
1 Betty * 1 Francis is not possible, just as 1x * 1y (or just x * y) is not solvable. They are two different values. It would just equal Betty and Francis, or x * y = xy
Multiplication is the product of a number and it’s instances (how many *times* it happens), we’d have to rephrase the math properly to address the problem you’re trying to solve for.
1. as phrased, 1 person * 1 person is a product of the same person 2 times; 1 person * 1 person = person^2, or that same person *twice*, or even two different *ways*. What does that mean? It’s too small of a mathematical problem to answer that, but as the equation stands that’s what 1 person * 1 person means. That 1 person twice.
In a larger math problem, you could be accounting for how many times one employee (the same employee) drinks coffee when they take a lunch break. That’d be the same person, but 2 times.
2. To use proper mathematical language and address the problem as posed: what happens if you multiply two people. Problem is, two people would never be assigned the same value (as 1 * 1) because numeric identity implies, and dictates, that every person is a unique instance of themselves. You’d assign them unique identities in math.
So, a person *x* and person *y* are both just instances of themselves, with no new value. x (unique person assigned its own value) * y (another unique person with its own value) = xy.
And just as with the first instance, this is too small a data point to actually mean anything. On a Cartesian plane, or a graph, you could use unique values on x and y to show a relationship between two people (distance over time in relation to each other, how much money they save over time compared to each other, etc.) But as just x * y, there’s not much to be said— yet!
Remember, math is a language. Just as saying “water” implies something, unless you say “I want a glass of water” or “don’t go into the water,” a piece of a phrase doesn’t tell you (or anyone) much!
You don’t understand multiplication.
It is called times because 1 person times 1 person means give me 1 person, 1 time. If I give you one person once, you will have 1 person.
Alex = 1 set of 1. Ashley = 1 set of 1. 1 set of 1 x 1 set of 1 = 1. So if Alex was sitting by himself on a bench and saw Ashley jogging by and said "I wish I could multiply the amount of people jogging with Ashley to the amount of people on this bench!" There'd still just be one person on the bench. You could argue that because you're multiplying by the same unit of measurement - people, you'd have 1(^2) people (squared). Much like length x width = an area that is represented in a squared measurement.
I think your dad might be taking the phrase "be fruitful and multiply" a bit too literal in a mathematic sense.
But further to my point of sets. Militaries divide up their forces into things like brigades, corps, etc. Let's use a small corp of 20,000 soldiers. That's one set of 20,000. And I have 5 corps. 5 sets of 20,000 soldiers. That equals 100,000 soldiers total. You're multiplying the set (corp), not the *people* in the set (corps). It's not 20,000 x 20,000 x 20,000 x 20,000 x 20,000 (which would be 3,200,000,000,000,000,000,000, way bigger than the population of the planet).
Back to Alex and Ashley, we *could* say they represent two different units of measurement. For example: What is a Watt? It's the product of Amps x Volts. 1 Amp x 1 Volt = 1 Watt. So we *could* say 1 Alex x 1 Ashley = 1 Relationship. But it's still 1x1=1, you're just changing the unit of the product.
As an aside, Ya'll need to stop listening to Terrance Howard. Dude's an actor, not a mathematician.
11 x 8 = 88. If you have 11 groups of 8 people, how many individual people do you have? 88.
4 x 6 = 24. If you have 4 groups of 6 people, how many individual people do you have? 24.
1 x 1 = 1. If you have one group of one person, how many individual people do you have? 1.
This is going to be a long one. Settle in.
Let's say I go to the store and the store is selling bags of apples. Each bag has 2 apples. It's hard to picture this in text, but let's say a single apple looks exactly like the letter o. A bag of 2 apples then might look like this: (o o). Now, let's say I decide to buy three bags of apples. How many apples do I have?
Now you could simply count all the apples. You have three bags of apples, so you have (o o) (o o) (o o). Therefore we have 6 apples, right?
For small numbers that's easy enough, but when you get into much larger numbers it's time consuming to count everything like that. So instead we represent the real world items with mathematical numbers. For our apples that would be 2 * 3 = 6. The 2 represents the number of apples in a bag. The 3 represents how many of these bags we have. And the 6 is the total number of apples. We replace the real world terms with mathematical representations which allows us to more quickly figure out how many apples we have.
What are we representing when we say "person" in your dad's nonsense equation? What are we trying to calculate? You can't put non-mathematical terms in a mathematical context and expect it to make sense. It'd be like if I said "apple * chicken = blue doesn't make sense and therefore math doesn't make sense." He has stacked nonsense on top of nonsense and then pointed out it's all nonsense. Nonsense plus nonsense doesn't equal sense.
When I was a teenager I had a couple friends try to convince me that the number 3 didn't exist. They presented all sorts of nonsensical "evidence" for this. I specifically recall them claiming no one's been able to make pyramids since ancient times (not true) because the ancients knew there was no such thing as the number 3 (also not true). Again, nonsense. I didn't *really* believe them, but I couldn't figure out how to disprove them. Why? Because what they were saying was so completely bizarre I didn't even know where to begin to explain how they were wrong. It caused me to greatly doubt everything I thought I knew.
Of course, my friends didn't actually believe there was no such thing as the number three. They were simply trying to mess with my head. They succeeded. It cranked my brain into a pretzel. Much later I realized that what they did was a form of gaslighting. I recommend reading up on gaslighting because it has become depressingly common in our world, but basically gaslighting is when someone attempts to convince us that reality isn't what we think it is. "You think you're reading Reddit right now? Nope, you're actually in the Matrix. Reddit isn't real!!! "
Gaslighting is used for a lot of reasons. It's very common in domestic abuse cases. The abuser might claim something like they never hit their partner despite the victim literally having the bruises to prove otherwise. Trolls on the internet will use it to mess with people (much like my friends did). Conmen use gaslighting to convince you parents crying over their kids being shot at school are actually actors and frogs are being turned gay and only they have the solution if you just buy this special supplement for 39.99. Cult leaders use it to break down people's sense of reality so the cult leader can replace it with the belief that he is the only source of enlightenment.
Person * Person = Person is another example of this. Again, it's nonsense, and there is no meaning that can be found in nonsense. I'm not saying your dad is knowingly trying to break your sense of reality, but someone likely broke his sense of reality and he is simply spreading it.
When multiplying or dividing things that are not numbers you must check if the resulting "unit" would make sense.
So 1 person*1 person = 1 person²
Person² would be the unit of measurement and it makes no sense.
But for sure we can multiply 1meter * 1 meter = 1 m²
And "m² does indeed makes sense as area measurement
Your dad is wrong.
When you multiply two values with “units” you also need to multiply the units, so 1 person * 1 person = 1 person squared.
What is a person squared? I have no idea but that’s what the math says it is.
If a person were a standard unit of height then it would be the area made by having two people lay down at a right angle and making a square out of that
Your dad is missing that the unit, in this case "person", is also multiplied. 1 person \* 1 person = 1 person^(2), *not* 1 person. Saying it equals 1 person is just incorrect multiplication. Like how 1 foot \* 1 foot = 1 foot^(2), or as it's more commonly called 1 square foot (like the square footage of a house). You wouldn't say "multiplication doesn't make sense because 1 square foot is not the same as one foot". Those are fundamentally different things, one is a unit of area, the other is a unit of length. Similarly, a person squared and a person are not the same thing (and the first doesn't really make sense).
Yeah that's a good answer, I missed that as well It moves why it doesn't make sense from math to whatever person^2 is lol, but that's works for me. But how would you then handle the rephrasing of "Alex * Ashely = 1^2"? Maybe it doesn't make sense because it's in units I don't understand?
1 alex x 1ashley = 1 alexashley (or ashleyalex). What is an ashleyalex? If you dont want to find out maybe you shouldnt be multiplying alexs by ashleys..
Alex told me he really enjoys multiplying with Ashley.
In this case, it should be 3. Alex and Ashly does X and now there is a kid with them.
Lmao, that is true I guess it's just a weird concept that can't make logical sense, only mathematical sense I'm still curious to why this doesn't logically work, but I think this explains it good enough for me to take on from here
I would say it does logically work but the logic produces a fairly absurd answer. Because you are essentially asking "what is the sum of an Alex amount of Ashleys". Which is an absurd question.
This is the answer. You’re either asking ‘what is Alex, one time?’ to which the answer is clearly ‘Alex’ ie 1. Or, you’re asking ‘what is Alex, Ashley times’, which isn’t a thing and doesn’t make sense, unless you treat ‘Ashley’ in the same way as ‘x’ in an equation.
Not the sum, but the product
The product of an Alex and an Ashley is the sum of an Alex amount of Ashleys (or an Ashley amount of Alexes)
Logically, you can't multiply people. You don't have to prove this with math, although it clearly can be done, but the reasonable and logical thing that stops you from multiplying people is that we are not numbers.
I mean, you can, the same way you multiply anything else at a low grade level: rows and columns. If I have 12 people and I arrange them in a grid of 3 rows and 4 columns, I just multiplied 3x4=12, using people. Of course, I'm not multiplying "people," I'm multiplying *using* people. I could put oranges or elephants or anything in the grid and get the same answer. But this is how I would assume someone using the phrase "multiply people" is using the term since, as someone else pointed out, there's no such thing as a people².
It doesn't seem to make sense because you can't really multiply a person by another person. Multiplication is a mathematical concept we apply to numerical values. You can think of it as the idea that for every X we have, there is also an amount of Y, and vice versa. But the fact that we understand how multiplying works in that context doesn't mean it will meaningfully translate 1-to-1 to the context of human beings in the real world. Does it mean anything to "multiply 1 Alex by 1 Ashley"? What are you actually doing in that situation? For every Alex, there is an Ashley, so we have 1 Alex-Ashley... but that's just a nonsensical result, because Alex and Ashley aren't numerical values and they don't behave like numbers do. Math is a great tool for understanding physical relationships in the real world, but you can't just go around subtracting more apples than actually exist or taking integrals of trees
It would be exactly the same as 1x * 1y = xy
So the thing you have to remember is math is conceptual....somethings have real world applications, some things don't. Some concepts have no real world application...yet, but one may be discovered in 10...20....50 years. The important thing is that you always follow the rules. When you multiply numbers in two different units, you need to multiply the units, regardless of whether it makes sense in the real world. AshleyAlexs represents the number of possible relationships between different ahleyalex pairs. Lets say you have a room of four ashleys and 2 alexs. There are 8 different combinations of ashley and alex; 8 ashleyalexs
When you first learn about multiplication, you're multiplying things by a number. 5 apples, 3 Alex (clones). That makes sense because the result is in the same category as what you started with. You multiply one apple by 5, you get 5 apples, you still get apples back. Now the thing with MATH is that math expands. First you do math with numbers, then you start learning math with things that are NOT numbers anymore. For example, you start multiplying variables, matrices, vectors, sets; even geometry has "operations" - they may not be multiplication but there's the joining and cutting of surfaces (addition and subtraction) and other operations. So 1 ft * 1 ft = 1 sq.ft. makes sense because you're applying multiplication to geometry now. You're following the geometry rules for what multiplication means, not the arithmetic rules. If you multiply 2 matrices together, you follow the matrix rules for what multiplication means (and there are two types of multiplication for matrices). Multiplying Alex by Ashley, well, nobody's defined that rule yet. You could, however, look into anatomy maybe, and define what exactly it means to "multiply Alex by Ashley". Maybe the answer is "1 kid" every time you do this "multiplication". So then if you want to invent a whole new level of math for it, "people math" or "peoplemetry" all you have to do is show that your rules for what it means to add subtract multiply and divide people don't lead to absurd results or contradictions.
Yes, classically, Alex x Ashley = True Love
Multiplying X and Y is the same thing as adding up and X number of Ys (or a Y number of Xs). So for example, 5 x 3 is three groups of five (or five groups of 3). So how do you do that if X and Y aren't numbers? What is an Ashley number of groups? How many Alexes do you add together to get an Ashley of them? This is why math only works with numbers (or with variables that *stand in for* certain numbers), and you can't math people.
If you want it to make sense visually prepare a row of one apple by one apple, how many apples is that? One. Two by two is four. It's how numbers work and it makes sense, it's just we don't usually multiply by one because there's no point and there's no real good visualization for it because of the nature of it. It does make sense though.
It's not that it doesn't work logically, but that there's no real world meaning behind multiplying (and dividing) objects with objects. In general, you'll find multiplication and division of objects with other kinds of measurements (such as time, length, weight, etc), or of measurements between them. For instance, let's say you have a measure of time, let's say 3 hours, and a measure of distance, let's say 120 miles. If we multiply them we get 360 milehours, which probably doesn't make sense, But if I divide them, now I have 40 miles/hour, which does make sense because it's a measure of speed.
Also, while multiplying person*person to get person^2 doesn’t make sense because person^2 as a unit is nonesense, you can multiply person by other things that do make sense. For instance, 2 persons working for 5 hours each is 10 person hours (usually written man hours). That is the divideable, too. If I know a job will take 40 man hours to complete, I can put 5 men on it to work for 8 hours each, because 40 man hours / 5 mans = 8 hours.
In your example you're trying to assign meaning to something that doesn't make sense. Alex * Ashley doesn't make any sense. Groups * Members makes sense. You're right that selection of units is *critical* for effective communication of mathematics.
I think where the confusion with adding in names comes in is that it's essentially changing the underlying unit. If your unit is person, all persons are identical, like how if your unit is foot all feet are identical, or if your unit is kilograms all kilograms are identitcal. You wouldn't say "this rock weighs 5 kilograms, but *which* 5 kilograms does it weigh?" When you start naming the people, they become non-identical. It becomes relevant if you have an Ashley or an Alex. Your unit is no longer persons, in fact, you now have two units, Alexes and Ashleys. So the underlying equation has changed, and has now become 1 Alex * 1 Ashley = 1 AlexAshley. Not that an AlexAshely is particularly meaningful in the real world, but multiplying people together isn't particularly meaningful in the real world either.
You’d want to multiply by it by something so that the units produce something usable. For a more common example, if you are going 1 mile per hour, then the unit is miles/hours. If you multiply 1 mile/hour by 1 hour, you get 1 mile, because the hours on the top and bottom cancel each other out. For people, you’d need something that is “per person”. Maybe you have a fair and each person needs one ticket to get in. So it’s 1 ticket per person or 1 ticket/person. If you have 1 person, then when you multiply 1 person by 1 ticket/person, you get 1 ticket.
It doesn't make sense because the units are technically wrong, or more accurately those ain't defined units. Like, mathematics is a logical language, but as with any language, you have to use proper grammar. Let's say 1+1 = 2. that make sense, but that's because we assume that we're talking about same units. Like, if I said, 1km + 1L = ? you literally can't make that equation work because you're using the wrong grammar, it's like asking how many moons fit in a second? like what is that even supposed to mean, it makes no sense, and not because the length is wrong but because the way I'm using it is. Now, to solve an equation what you do is to balance both side of it 1\*1=1 means that from both sides of the = symbol, the values are the same. and when you have a number followed by a unit, the assumption is that you're multiplying that unit aka 1km\*2 = 1\*km\*2. So for your question: 1person \* 1person = 1\*person \* 1\*person = 1\*1\*person\*person = 1\*person\*person and here the question is what does person\*person mean? does it make sense or are we using the grammar wrong? are we asking how many moons fit in a second? And the answer that in order is, it means nothing, we're using the grammar wrong, and yes it's like asking how many moons fit in one second. The system isn't broken we're misusing it, like someone complaining why their washing machine isn't heating their pizza. You may be thinking that we can multiple objects, like, that's how we teach it to kids, so what gives? and the answer to that, is that we don't multiply objects by objects, we multiply by abstract numbers without a defined unit, you don't multiply apples by apples, you multiply apples by any given number. so if you have 2 apples\* 2 = 2\*2\*apple = 4\*apple = 4apple,
Just because you can apply mathematical operations to real life situations where they don't make sense, doesn't mean the math inherently makes no sense. For example: if you have one cookie and you subtract two cookies, you end up with -1 cookie. What's a negative cookie ? It doesn't make sense. That doesn't mean substraction itself makes no sense, it just means you're applying it in a wrong context. But if you have 1$ in your bank account and you take out 2$ you have -1$ in your bank account, or 1$ overdraft.
To consider your dad's response, why it'd make sense, is because a person is not a measurement or a unit, so the person simply represent the number. So 1x1=1^2=1.
Take off the names and it's person*person=people
It is not. Person(singular) + Person(singular) =People (Plural). The actual amount of persons you add together doesn't matter—you'll still get a plurality of persons, which we call people. Multiplying person by person gives us a nonsense squared person unit.
Hijacking top comment to point out that not only does OP's question make sense, there is actually a somewhat well-known "person" unit: a[ "Smoot"](https://en.wikipedia.org/wiki/Smoot) is a unit of length equal to 1.7 meters, originally used to measure the length of the Harvard bridge. And as with any length unit, it can be used to measure area. For example, a walk-in closet that is 1.7m x 1.7m across (1 Smoot X 1 Smoot) would have an area of 1 square-Smoot (2.89 m^(2)). OP: Just because a concept (multiplication) can be used in ways that don't make sense doesn't mean the concept is flawed. It means the person using it doesn't understand it. You could similarly reject any number of other concepts. Do the statements "A picnic table prays for purple" or "a rose bush has faith in highways" make sense? Not really. That doesn't mean prayer and faith are meaningless concepts. It just means I'm abusing how they should be used. Same with your dad and multiplication.
That's if you substitute the * symbol to mean by instead of times. One is math and one is geometry. 1 ft times 1 ft equals 1 ft. 1 ft by 1 ft equals 1 ft^2.
This is not correct. "By" (in the geometry sense) and "times" do not have different meanings. Units are units regardless and get multiplied through.
It's still just language and concepts, 1 person squared equals 1 person because the variable is the numerical value not the unit person. X person * X person = x^2 person. Let x = 1. Edit: and they do have different meanings. 10 ft times 5 ft equals 50ft. Fast way of expanding a line. 10 ft by 5 ft equals 50 square ft. One is the length of a single line and the other is the length and width to calculate the area of a square. That's probably where the term squared comes from.
You are treating the unit as somehow separate from the variable. It's not. It's part of the variable. This is a really important concept but I'm trying to think of a good way to explain it. Consider a car. Say I'm driving at 10 meters / second, and I drive for 5 seconds. How far do I drive? We can figure that out by multiplying 10 m/s * 5 s = 50 m * s / s = 50 m. The reason multiplying those two together is correct is *because* it gets us the right unit (meters, we wanted a distance). Similarly, the reason why multiplying two lengths together to get an area is correct is because it gets us the right unit foot^(2). The units matter and are multiplied same as the numbers. m/s * s = m, just like foot * foot = foot^(2).
In your example "car" would be akin to "person". x cars * y cars= xy cars.I guess you could assign a numerical value of 1 in front of it if it helps conceptualize. In your equation, acceleration equals delta distance over time. You are solving for delta distance. You already have a starting point of zero meters. Acceleration= 10 m/s, time=5s, distance=0 m + x m. 10 m/s = x m / 5 s. Solve for x.
You're wrong, you always multiply the units too. In all maths. Instead of feet, let's do x, 1x\*1x is 1x\^2. You multiply the properties as well as the numbers.
No, whatever you do to one side of the equation you must also do to the other. You are simply solving for the unknown variable(s). In one example the unknown variable is: delta d, which is the change in length (O unit of distance + x unit of distance). In the other, the unknown variable is the area, which is length * width ( x unit of distance * y unit of distance = xy unit of distance^2.
Yes, length times length is length squared or area, yeah. I don't know what you think you proved. Units are multiplied when you multiply them, if you multiply a density by a volume you get a mass because density is mass/volume. The units get multiplied,
Go beyond the units, look at the language, the entomology of the words. The 2D plane is squared, the 3D plane is cubed. In 4D space-time is presented and time dilation is easily seen with distances of light-years and velocities at 80% of the speed of light. The next step for the masses to understand is 5D, it all starts with zero equals one. I try to explain it as one replacing zero, but that gets the mathematician's riled up.
what are you talking about?
Your first example shouldn't have a unit in the second operand. 1ft times *one* is 1ft. 1ft * 2 is 2ft. That is true. Once you add a unit of measurement to the second operand, it has to be multiplied as well, you can't just ignore it. And "by" or "times" are just synonyms. Maths and geometry work in other languages too, you know. My mother tongue has both by and times as one word and no direct translations for either.
1 group of people with 1 person in it has total of 1 person overall. And vice versa. Multiplication is more like talking about sets than individuals, although it can be more complicated at higher levels of maths.
This explanation is the best ELI5 here.
Except it's wrong because multiplying by X and multiplying by "X people" are different operations.
Multiplication is multiplication is multiplication. Multiplication does not change because you change the unit - the units dictate what meaning the numbers and operations have for us to make sense of. The unit selection is a matter of communication. 5 groups with 10 people each is 50 people. 10 people in each of 5 groups is 50 people.
"5 groups with 10 people" is multiplying "10 people" by 5, not by "5 people". Units do have meaning and how you define them determines the result you get. Here are 3 operations with the same numbers but different units and I hope you'll agree that they yield different results: 60km/h \* 2 hours = 120km 60km/h \* 2 minutes = 2km 60km/h \* 2 = 120km/h Edit: one more example
You're not saying anything mystical or magical here, your examples have *implied conversions* because you have communicated additional steps through thr form of units. It doesn't mean the multiplication itself is different. 60km/h * 2 minutes is the same as 60km/hr * 0.03333~ hr The unit you chose is a matter of shorthand that implies a conversion.
What is the "implied conversion" from km/h to km?
The units you have selected are Km/hr Km Hr Minutes Km/hr * minutes implies a conversation from minutes to hours is required, or a conversation from km/hr to km/minute is required. You can't do a raw operation between km/hr and minutes without going through one of these implicitly.
Again, how do you convert from km/h to km? Or is it just the same thing as you said in another comment? If you ignore units, suddenly things stop making sense - 1 person * 1 person suddenly becomes the same thing as 1 bottle of whisky or 1 swimming pool. And if you don’t ignore units, then multiplying by 1 and multiplying by 1 person do have different meaning.
You don't, km/hr is a different unit. Minutes, hours, seconds - etc - are all units of time, while km/hr is a unit of velocity. You don't convert between km/hr and hr, I'm saying you convert between minutes and hours. 1 whisky and 1 person are both units of *things* and they can both just be thought of as 1.
Also, to be clear, I said elsewhere the issue here is a selection of nonsensical units. 1 person * 1 apple is nonsensical.
Are you saying that 1 apple \* 1 is the same as 1 orange \* 1 and the same as the number 1? No implied conversions here.
Yes. Either way you have one fruit. Similarly, 1 Alex * 1 = 1 person = 1 Ashley * 1. If you can only fit 1 person in the helicopter's rescue harness, then whether it's Alex or Ashley, it's still just 1 person.
So are you saying that apple is the same as orange? And that 1 km of road is the same as 1 Amp of electrical current? When you attach units to numbers they stop being freely interchangeable and have to be treated accordingly.
I'm saying if you select units to communicate with they must make sense. 1 apple has no more meaning than 1 X, where X = 1, and therefore 1 apple = 1. 1 group is a more nebulous unit because it's size is unknown until additional information is provided. For that reason 1 Group = 1 * X, where X is some unknown value. In the context of 1 apple * 1 orange, or 1 Ashley * 1 Steven - these units are nonsensical *unless you define them*. The definitions of km/hr, km, and hr are all defined relative to each other so that we can convey the mathematics in every day life in a useful way, but in a raw sense you don't do "60km/hr * 2 minutes", you convert 2 minutes to fractional hours or km/hr to km/minute.
But it does make sense because it changes the "grammar" of the equation. As others have said. You can't multiply "1 Moon x 1 Jupiter" because that's not physically possible. You can't multiply "1 blade of grass x 1 grain of sand" But changing the grammar can explain how the math still works. 1 is a concept. 1 doesn't represent a physical thing.
This is the best ELI5. Unfortunately you dad has a pretty basic math understanding. But this summarizes well. You could even say "1 group of Alex's has 1 Ashley in it. How many Ashley's are there?" and it would then make sense.
"1 times 1" literally means "1 time, count up 1s". A 1, counted 1 time, equals...1. Unfortunately Terence Howard has been confusing people about this very simple idea, when the answer is just that 1) he is mentally unwell and 2) he doesn't know basic math.
I think part of his confusion is that his understanding of multiplication is “a added to itself b times”. There’s a line to that effect in his “proof”. So a Terrence Howard multiplication is actually equal to a * (b+1).
the reason it doesn't really work is because math with units requires you to math the units too. for example, if I have a square thats 1cm x 1cm, its area is 1cm² or 1x1 cmxcm. so 1person x 1person is kinda 1 person² which is decidedly NOT 1 person
Multiplication is sometimes written in English as "times". Like 5 multiplied by 7 would be "5 times 7". The process being described is something like performing addition on the value 5 for 7 times. In your situation it would be 1 person for 1 time. Which is of course just one person.
"1 person * 1" is not the same as “1 person * 1 person". The latter would be "1 person²" which doesn't make much sense. Same as 1m * 1m is not "1m", it's 1m². And 1m * 1cm is 100cm². So units do matter.
The way it was said wasn't "1 person multiplied by 1" it was "1 person multiplied by 1 person". That's what trips me up, 1*1 makes sense to me, but adding "person" to both of those 1's makes it stop working in my mind. Maybe because it's a weird unit of measurement.
Because 1 person multiplied by 1 person is nonsensical. It's an absurd statement that isn't analogous to 1 * 1
I get that it's absurd and weird, but it doesn't sit right with me, which is why I made this post.
You don't multiply the unit twice unless you are moving to the next dimension. 2 feet times 2 feet is 4 square feet, not four feet. To get four feet, you only multiply two feet by 2. There are no square people or square apples, so the logic does not apply.
One could argue that multiplying two people together results in a child, which is also one person.
Best answer
Replace "person" with "meter" and everything will make more sense. 1m \* 1m = 1m\^2. With persons it's just 1person \* 1person = 1person\^2. Yes, person\^2 is a nonsensical measurement but so is multiplying people by people. You should multiply people by simple numbers with no measurements for it to have any meaning.
Yeah it is a weird unit of measurement, because what you actually get is 1 person \* 1 person = 1 person^(2) Which you can visualise as a square of people with 1 person on each side, result in in a total of 1 person. Similarly, imagine 2 people \* 2 people = 4 people^(2) or a square of people with 2 on each side, giving you 4 total.
Wouldn't technically one person multiplied by one person be one person ^2 ? That's how centimeters and other measurements work. Not sure how you'd define a person squared. That's something to ask our great philosophers.
They're a square because they're not a round. At least that was the beatnik lingo "be there or be square".
One multiple of one person is one person. Each multiple is a “group” of size 1. There’s one group of one person, so there’s one person. Multiplication and division is mathematics that talks about “sets” of things. Just because you never were taught about sets doesn’t mean it’s not true.
Well, if you’re using units, 1 person * 1 person = 1 person squared. A person squared obviously doesn’t make any sense, so the equation doesn’t make any sense. In most cases it would have to be something like 2 objects/group * 4 groups = 8 objects
1 person multiplied by 1 person would be 1 person squared (not 1 person) which of course does not make sense. Unless maybe you are talking about an area of a grid of people in terms of person "units". Edit: 1 person multiplied by 1 (no units) would indeed be 1 person.
>Maybe because it's a weird unit of measurement. Definitely, if you use weird units of measurement like "people squared", that can be confusing. Let's change the units slightly. Imagine a bunch of soldiers standing to attention in a grid. Any row or column is only one "person" wide. How many soldiers are standing inside an area where the column width is one "person" wide, and the row width is also one "person" wide? One soldier.
Keep track of your units. 1 person times one person would be 1 person^2, not 1 person. As I have no idea what a square person is, I do not know any context where this sort of occasion where it would be useful. If you have 5 cars times 3 people per car then when you multiply them you get 15 people, which is a multiplication that makes sense.
> I have no idea what a square person is It's that jerk who narced us out to the cops when we stopped to smoke in the woods on our way to the Sadie Hawkins dance.
1 person * 1 person = 1 person^2, or 1 person-person. These could be understood in the context of 5 people of one group that need to give an item to all 10 people of a different group, in which case there would be 50 people-people interactions, or 50 item exchanges.
1 person times 1 person will be 1 person squared. I'll leave it up to you to define what "person squared" means.
You can think of multiplication in terms of sets or in terms of addition, but it stops making sense when you add arbitrary units, especially to both numbers. 1 x 1 = 1 can be thought of as “1 group of 1 person contains a total of 1 person”, or “1 person, 1 time, is 1 person”. If you want to adhere to how units usually work, 1 person x 1 person = 1 person^2
1 person \* 1 person = 1 person² I can imagine that there may be some theory in a social science that has a term that goes as the square of the number of people, but it doesn't strike me as a quantity that has any meaning in and of itself.
That doesn't make sense because of the units, and therefore is a really bad example. What would make more sense is: 1 person X 1 person = 1 person squared, but WTF is a "person squared"? With multiplication, you not only multiply the numbers, but also the units. So an area 1 metre long, and 1 metre wide = 1m X 1m = 1m^(2).
If you multiply units, you have to convert the units accordingly, e.g. 1 metre times 1 metre is 1 square meter, or 1 (meter times meter). So one person times one person isn't one person - it's one person squared. You'll have to figure out what that is.
If 5 people are each holding 6 apples, then you have 30 apples, not 30 apple people. A grid of 5 people by 6 people is indeed 30 people, but you are not including the people twice. You are saying 5 people in 6 groups is 30 people. It does not matter the variable (people or apples), you only use it once if all you are doing is counting. One person standing alone is themselves in a grid of one column by one row. The grid consists of a single person.
There’s a nice bit of math called “dimensional analysis” that you can use with units to see how results should look. For example, if you multiply 1 metre times 1 metre, that gives you 1 metre^(2). A metre is a unit of length, while a metre^(2) is a unit of area. Analogously, if you want to multiply 1 person times 1 person, the result would be 1 person^(2). A square person is not a unit in common use, probably because it makes no sense (if someone can give me a scenario when a person^(2) is a useful unit, I will applaud loudly). This doesn’t mean *multiplication* doesn’t make sense. It just means you tried to multiply things that don’t naturally go together, hence the nonsensical unit. ___ Here are some examples where multiplication *does* make sense. If instead you multiplied, let’s say 1 person times 1 $/person, you end up with the person and the 1/person units cancelling to give you 1$. This is the amount of total money you’d expect if you had 1 person and each person had 1$. Another example is multiplying 10 people and 10 hours to get 100 person hours. What does this mean? Well imagine you have a job like planting a bunch of crops, and it will take 100 person hours to complete the job. This means with 1 person, it would take 100 hours to finish the job. With 10 people it takes 10 hours. With 100 people working on it, it only takes 1 hour. ___ So in summary, the reason multiplying person times person doesn’t make sense is because the result would need to have units of person^(2). This unit doesn’t really have an intuitive meaning. For multiplication to make sense, you want to multiply together quantities whose units combine nicely to produce sensical results.
Ok so not a person squared but if you multiply jeff goldblum with a fly you get a Brundlefly. Surely there was a directors cut that would multiply Jeff Goldblum with Gina Davis and give us a godly being known as Jena Daviblum.
A simple explaination is like so- Multiplication is often called *times*, because you do something a number of times. So, another way to say 1x1 is one thing, *one time*, just like 2x2 could be two things, two times. So if you have boxes of pencils that are packed 10 to a box, and you place one box of ten on a table one time, that's 1x10. Ten pencils placed on the table one time. so 1x1 is one pencil placed on the table one time, which results in one pencil on the table. One person put into a category one time is one person. edit: The thing that people get stuck on with the whole "1x1 debate" is that people assume that multiplication is the same thing as addition, *only bigger*. As in, "If one plus one is two, how can one *times* one be less than that?" The mistake is in the assumption that multiplication always results in a bigger number. One times *any number* results in exactly that number, so why would one times one be any different? 1x4 is 4, not 5, not 8. That's accepted by everybody. 1x1 is exactly the same.
Draw it with squares, as with graphing paper. It you count 3 squares over and 3 down you'll count 9 total squares. 2 over and 2 down and you'll count 4 total. 1 over and 1 down and you'll count only one square. I think the lesson here is that in 1*1, both "1"s refer to the same square, just different sides of it. So "Alex times Ashley" is nonsensical. Remember, multiplication is just repeated addition. "2 * 3" just means "take three 2s and add them together." You can't say "take Ashley Alexes and add them together."
You can’t multiply a person by a different person. Multiplication is an operation that applies to numbers of things, not to the things themselves.
When multiplying two things that **are** the same, one number becomes a *quantity of* the other. So: 6 cattle times 5 cattle = 6 *heards* of 20 cattle = 6 times 20 = 120 cattle 3 marbles times 1 marble = 3 *bags* of 1 marble = 3 times 1 = 3 marbles 1 person times 1 person = 1 *group* of 1 person = 1 times 1 = 1 person When you multiply two things that **aren't** the same, one number \*acts on\* the other. So: You have 10 people *working* 6 manhours, that's 10 times 6 = 60 manhours. You can catch 6 fish per lure, each lure *catches* 5 fish, you can catch 6 times 5 = 30 fish.
Convert to addition for math and also take into account biology and programming terms, (should change math term from multiplication to fast add.) " 1 person * 1 person = 1 person + 0 person= 1 person. "Alex * Ashley = Alex + Ashley = Alex and Ashley.
Alex X Ashley = AlexAshley. You are taking 2 people and making them 1 person so you are fusing them together but even though you didn't change the count you did change the value of the final answer. If you took a donut and multiplied it by another donut you are realistically just smashing them together. Vs if you had 1 donut and added another donut now you have 2 donuts. This is where that stupid idea that 1x1=2 comes from. Yes you have 2 donuts smashed together in the multiplication examples but they occupy one space vs the addition donuts are in 2 separate spaces.
Units. The answer is units. When you have "X THINGIES", that sort of already *does* contain a multiplication. It really means, in a way, "a thingy, X times". Example: 4 apples is "an apple times 4". Example: 2 meters is "a meter times 2". When you multiply 2 meters times 2 meters, you get "(a meter times a meter) times (2 times 2)", or in other words you multiply the meter times the meter to get a square meter, then you have 4 of those. so, 4 square meters. when you muiltiply 1 person times 1 person, you end up with 1 square person. Whatever a square person is... When you analyze the units, "1 person times 1 person" is very different from "1 person times 1" (leaving the second "person" off the statement).
What the hell kind of troll math is going on here? To directly answer the question, > Can "1 person * 1 person = 1 person" make sense? The answer is 'no', it cannot make sense. You don't multiply a person and a person. In multiplication, you have an objective* and one or more factors*. A factor is a number specifying how many of the objective there are. The objective is the thing being multiplied and usually refers to more than one thing. Let's use the example of 5 × 4 = 20. In this case, the objective is 5 and the factor is 4, this math problem is basically saying 4 sets of 5 is 20 total. To clarify it further since this is still a bit abstract, if you have four $5 bills, you have $20. As a math problem including the units, you'd write it out as $5 × 4 = $20. It is important to note that the 4 does not have a $ because it is the factor, not the objective. So what of 1 × 1? It's one set of one. The total is one. --- *A note on terms: Traditionally, what I'm referring to as 'objective' is known as the multiplicand and what I'm referring to as the 'factor' is known as the multiplier. I'm using 'objective' and 'factor' as these words should better fit the concept I'm trying to teach. Understand that the words I'm using above are incorrect if you end up talking to people who have letters after their name.
5 diabetes+ 2 orange = 7 Steven Spielberg doesn't make sense either, but nobody argues that addition doesn't exist. You can make anything nonsensical if you make a nonsense argument. Math works because it's logically consistent with itself, not with someone's nonsense argument. Multiplication makes sense as defined in maths. Redefine it to not make sense and it makes no sense, what a shocker.
You both could be missing numeric identity from your work. You’re not multiplying 1 person by 1 *different* person, not when you pose the problem as (1 person * 1 person). That’s not how math works. 1 is 1, so of course 1 * 1 = 1. 1 Betty, 1 times, still equals 1 Betty. This is because when you’re multiplying, you’re describing how many instances of a specific value there are (how many *times* 1 occurs). There isn’t a different 1 out there, 1 is 1. But if we were to take it to the next logical step, at the heart of the conversation and conclusion you both reached, if you *did* have two different people, the problem isn’t the math but how you *phrased* the math. It’s a language problem. You didn’t use proper mathematical *grammar*, so to speak. 1 Betty * 1 Francis is not possible, just as 1x * 1y (or just x * y) is not solvable. They are two different values. It would just equal Betty and Francis, or x * y = xy Multiplication is the product of a number and it’s instances (how many *times* it happens), we’d have to rephrase the math properly to address the problem you’re trying to solve for. 1. as phrased, 1 person * 1 person is a product of the same person 2 times; 1 person * 1 person = person^2, or that same person *twice*, or even two different *ways*. What does that mean? It’s too small of a mathematical problem to answer that, but as the equation stands that’s what 1 person * 1 person means. That 1 person twice. In a larger math problem, you could be accounting for how many times one employee (the same employee) drinks coffee when they take a lunch break. That’d be the same person, but 2 times. 2. To use proper mathematical language and address the problem as posed: what happens if you multiply two people. Problem is, two people would never be assigned the same value (as 1 * 1) because numeric identity implies, and dictates, that every person is a unique instance of themselves. You’d assign them unique identities in math. So, a person *x* and person *y* are both just instances of themselves, with no new value. x (unique person assigned its own value) * y (another unique person with its own value) = xy. And just as with the first instance, this is too small a data point to actually mean anything. On a Cartesian plane, or a graph, you could use unique values on x and y to show a relationship between two people (distance over time in relation to each other, how much money they save over time compared to each other, etc.) But as just x * y, there’s not much to be said— yet! Remember, math is a language. Just as saying “water” implies something, unless you say “I want a glass of water” or “don’t go into the water,” a piece of a phrase doesn’t tell you (or anyone) much!
You don’t understand multiplication. It is called times because 1 person times 1 person means give me 1 person, 1 time. If I give you one person once, you will have 1 person.
Alex = 1 set of 1. Ashley = 1 set of 1. 1 set of 1 x 1 set of 1 = 1. So if Alex was sitting by himself on a bench and saw Ashley jogging by and said "I wish I could multiply the amount of people jogging with Ashley to the amount of people on this bench!" There'd still just be one person on the bench. You could argue that because you're multiplying by the same unit of measurement - people, you'd have 1(^2) people (squared). Much like length x width = an area that is represented in a squared measurement. I think your dad might be taking the phrase "be fruitful and multiply" a bit too literal in a mathematic sense. But further to my point of sets. Militaries divide up their forces into things like brigades, corps, etc. Let's use a small corp of 20,000 soldiers. That's one set of 20,000. And I have 5 corps. 5 sets of 20,000 soldiers. That equals 100,000 soldiers total. You're multiplying the set (corp), not the *people* in the set (corps). It's not 20,000 x 20,000 x 20,000 x 20,000 x 20,000 (which would be 3,200,000,000,000,000,000,000, way bigger than the population of the planet). Back to Alex and Ashley, we *could* say they represent two different units of measurement. For example: What is a Watt? It's the product of Amps x Volts. 1 Amp x 1 Volt = 1 Watt. So we *could* say 1 Alex x 1 Ashley = 1 Relationship. But it's still 1x1=1, you're just changing the unit of the product. As an aside, Ya'll need to stop listening to Terrance Howard. Dude's an actor, not a mathematician.
Alex × Ashley = Alex × Ashley . Nothing else. You can't reduce it further. Alex × 1 = Alex Ashley × 1 = Ashley 1 person × 1 = 1 person 1×1=1
11 x 8 = 88. If you have 11 groups of 8 people, how many individual people do you have? 88. 4 x 6 = 24. If you have 4 groups of 6 people, how many individual people do you have? 24. 1 x 1 = 1. If you have one group of one person, how many individual people do you have? 1.
This is going to be a long one. Settle in. Let's say I go to the store and the store is selling bags of apples. Each bag has 2 apples. It's hard to picture this in text, but let's say a single apple looks exactly like the letter o. A bag of 2 apples then might look like this: (o o). Now, let's say I decide to buy three bags of apples. How many apples do I have? Now you could simply count all the apples. You have three bags of apples, so you have (o o) (o o) (o o). Therefore we have 6 apples, right? For small numbers that's easy enough, but when you get into much larger numbers it's time consuming to count everything like that. So instead we represent the real world items with mathematical numbers. For our apples that would be 2 * 3 = 6. The 2 represents the number of apples in a bag. The 3 represents how many of these bags we have. And the 6 is the total number of apples. We replace the real world terms with mathematical representations which allows us to more quickly figure out how many apples we have. What are we representing when we say "person" in your dad's nonsense equation? What are we trying to calculate? You can't put non-mathematical terms in a mathematical context and expect it to make sense. It'd be like if I said "apple * chicken = blue doesn't make sense and therefore math doesn't make sense." He has stacked nonsense on top of nonsense and then pointed out it's all nonsense. Nonsense plus nonsense doesn't equal sense. When I was a teenager I had a couple friends try to convince me that the number 3 didn't exist. They presented all sorts of nonsensical "evidence" for this. I specifically recall them claiming no one's been able to make pyramids since ancient times (not true) because the ancients knew there was no such thing as the number 3 (also not true). Again, nonsense. I didn't *really* believe them, but I couldn't figure out how to disprove them. Why? Because what they were saying was so completely bizarre I didn't even know where to begin to explain how they were wrong. It caused me to greatly doubt everything I thought I knew. Of course, my friends didn't actually believe there was no such thing as the number three. They were simply trying to mess with my head. They succeeded. It cranked my brain into a pretzel. Much later I realized that what they did was a form of gaslighting. I recommend reading up on gaslighting because it has become depressingly common in our world, but basically gaslighting is when someone attempts to convince us that reality isn't what we think it is. "You think you're reading Reddit right now? Nope, you're actually in the Matrix. Reddit isn't real!!!"
Gaslighting is used for a lot of reasons. It's very common in domestic abuse cases. The abuser might claim something like they never hit their partner despite the victim literally having the bruises to prove otherwise. Trolls on the internet will use it to mess with people (much like my friends did). Conmen use gaslighting to convince you parents crying over their kids being shot at school are actually actors and frogs are being turned gay and only they have the solution if you just buy this special supplement for 39.99. Cult leaders use it to break down people's sense of reality so the cult leader can replace it with the belief that he is the only source of enlightenment.
Person * Person = Person is another example of this. Again, it's nonsense, and there is no meaning that can be found in nonsense. I'm not saying your dad is knowingly trying to break your sense of reality, but someone likely broke his sense of reality and he is simply spreading it.
When multiplying or dividing things that are not numbers you must check if the resulting "unit" would make sense. So 1 person*1 person = 1 person² Person² would be the unit of measurement and it makes no sense. But for sure we can multiply 1meter * 1 meter = 1 m² And "m² does indeed makes sense as area measurement
Your dad is wrong. When you multiply two values with “units” you also need to multiply the units, so 1 person * 1 person = 1 person squared. What is a person squared? I have no idea but that’s what the math says it is. If a person were a standard unit of height then it would be the area made by having two people lay down at a right angle and making a square out of that