bmks270 said:

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That's philosophy, not math.

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No, it's not. When you deal with mathematical application, these are the kinds of questions you have to answer.

The idea of measuring and modeling IQ or intelligence is another great example from Carr. You can get a score of 110, but what that represents is nothing more than a subjective abstraction of how intelligent someone is. Yes, there is a standardized way to arrive at that, but that process is still subjective. Just because you arrived at the IQ score with objective math doesn't make it an objective measurement. In the same way that adding non-random numbers to a list of random numbers still produces random numbers (depending on the magnitude of the difference), using objective math in a subjective process still produces a subjective result. In linguistic terms, just because you used objectively correct grammar doesn't mean you accurately described reality.



ETA

And back to the apple example...

How you measure apples can be highly dependent on the math you use. Are you measuring apples as discreet units and using discreet math? In that case, 1 whole apple is equal to a half eaten apple is equal to 1 rotten apple and you have 3 apples, even though that is not reflective of reality. If you're using continuous mathematics and real numbers, you might say you have 1.5 apples. Both are objectively correct and legitimate, objective math, but they yield different results because you are using objective numbers subjectively to describe something.

You can say the discreet example is BS because those are different things and you have 1 of each, which is also true, but that proves the point of math being a abstraction. You have 1, but one what? The numerical definition of 1 is absolute, but the application and what or represents is not.

The best way I can think to put it is that mathematical variables are to numbers what numbers are to reality. A variable is an abstraction that represents something mathematically (number, set, line, curve, distribution, etc) in the same way that a number is an abstraction of something in reality (apple, car, boat, house, etc).

If you read the article in the context, then yeah, it makes sense.

He used a shocking example to get people talking....which he did.

Snopes Rates Biden's Claim That 2+2=5 As 'Mostly True'

Quote:

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"Sure, Biden got some key details wrong," said Bob Snopes, founder of Snopes. "But the central concept of what he was saying, that two numbers put together make another number, was completely accurate. Sometimes two and two make four. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. It is not easy to become sane."

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1872walker said:

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FFS, this is why you end up with a worthless college degree and hundreds of thousands in student debt. Choose a path in STEM and be a productive member of society rather than a leech on it's resources.

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How do I know that's how you spell Reely?

Following the responses on twitter is interesting. It is all what ifs, yes but, and philosophical back and forth.

He then presents the following "visual" explanation -

Trying to follow the philosophical oral gratification they are giving themselves - it appears the answer is 1 not 5. The placement of the 4 individual pieces into a single entity is 1 stable form which is the only way he can count the outer box. If one individual piece is removed, then the form will fall and no longer be in existence

I wish math was an abstract back in high school, I might not have had to take Algebra II in summer school. I could have just called my teacher a racist every time she said I was wrong.

pacecar02 said:

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response to the article:

Because they are not talking about math. This article talks about math as an expression in data science and how an expression is derived from real world data. Really, an improper expression was used.


The article is kind of mundane and stupid. If one oversimplified their expression to where only a single outcome was possible when multiple actual outcomes were probable, then that's where you failed.

Why is there an article written on this?

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Same reason as most journal articles from PhD students: mental masturbation.

two minutes late after all this time. ohwell

Madman said:

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If I owed him $5,000 and handed him $4,000 would he accept the debt as paid in full? Nope, thus we know he doesn't believe his own BS.

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How do you even know you owed him $5,000? Who calculated that?

Ciboag96 said:

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Here's a word problem:

Johnny takes his AR-15 to Portland to do some sightseeing and light shopping. He is assaulted by 2 masked Antifa members wielding Molotov cocktails and skateboards. Johnny defends himself by shooting each Antifa members twice. How many entry wounds will be the emergency room nurse count upon their arrival in the back of a third Antifa members rented Prius?

Harvard PhD student: FIVE!

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Perfect example!!

One of the antifa goons was in the act of trying to grab the gun from Johnny, therefore having the round pass through his hand before traversing his torso. Thus, the number of exit wounds would be greater than shots fired.

2+2=11

YouBet said:

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Future communist Kareem Carr is a dumbass that needs to go back to kindergarten.

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He's solution is looking for a problem.

troy_y said:

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Following the responses on twitter is interesting. It is all what ifs, yes but, and philosophical back and forth.

He then presents the following "visual" explanation -

Trying to follow the philosophical oral gratification they are giving themselves - it appears the answer is 1 not 5. The placement of the 4 individual pieces into a single entity is 1 stable form which is the only way he can count the outer box. If one individual piece is removed, then the form will fall and no longer be in existence

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This.

Sliver on the East Side said:

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Cassius said:

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PhD student...

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Future university president

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Future member of the dumbsh&t Hall of Fame.........his bust will be right next to Michael Young.

How are we up to three pages of this nonsense?

Cassius said:

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PhD student...

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Not All Dr's are created equal.

and nowadays anyone willing to go into enough student debt can become a dr.

I disagree. You are just taking an objective truth that is mathematics and introducing subjective definitions or hidden or mixed units and pretending it has meaning. It's the same thing as saying 2 + sadness = hairy.

Those same arguments also mean anything means anything. Which is useless, or maybe just to sound smart by confusing people.

It's all philosophy and effective at nothing other than to excite your imagination. It is fantasy disguised as reality. It's a lie in the skin of the truth of mathematics.

It's deception defined.

ABATTBQ11 said:

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After reading the article, OP has taken it way out of context. Carr makes some very good points. I think the comparison to language is the best.


Math is no different than language. It has representations of things, if you can consider numbers similar to words, and it has set rules. In the same way we have rules for sentences, tense, conjugation, etc, math has rules for how numbers are put together and manipulated to create meaning or approximate ideas. There is objectively correct language, just as there is objectively correct math. However, the application of language to describe something is highly subjective, and in that same vein, the application of math to describe something can be highly subjective too.

There are 200k-300k words in the English language, depending on if you count words that are rarely or not used. That allows English speakers to approximate highly abstract ideas to each other. However, those are still just approximations of the idea held. I can say I want you to paint a room blue with a specific idea of what the room should look like, but my statement to you is very broad. There are numerous shades of blue. Navy? Azul? Robins egg? What kind of paint? Glossy? Semi-gloss? Eggshell? With more specific words, I get closer to communicating my specific idea, but everything I say to you is still only an approximation and translation of the reality I want to create.

Applied math is much the same way. The numbers used to represent reality are only representations and often approximations. Any mathematical model, even for something fairly well understood like gravity, is only an approximation. How you define what a number represents is subjective, even if the numbers themselves and the rules of mathematics are objective. If I'm holding an apple and ask you how many apples I'm holding, you could say I'm holding 1 apple, and that is true. However, that apple has many seeds in it. By a different interpretation, you could say I'm holding infinite apples because that apple can reproduce given time and nutrients. You could also say I'm holding x apples as a function of t and model how many apples that apple could turn into over given periods of time based on many factors.

From a pure mathematical standpoint, 1=1, but an apple may not equal 1 apple. It truly depends on the mathematical abstraction of what an apple is and how an apple in my hand is represented mathematically. Calling it 1 apple is the equivalent of wanting a blue room. Calling it x apples at time t with a list of assumptions is wanting a room painted azul with an eggshell finish, off white trim and switch/outlet plates, and a smooth ceiling. They are very different, but also the same.

The more general you get, the more objective math becomes until it is completely objective. However, the more specific you get, the more abstract and subjective it becomes. For someone working in it, it is a very important nuance.

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The definition of an apple would have seeds built into it. One apple is one apple.

2+2 deals with definitions of mathematical objects, not gravitation. According to their definitions 2+2=4. That's all there is to it.

Let's not get bogged down in nonsense like does 2+2=5

Let's get into the good stuff (and yes, this is actually really cool and worth a watch)


And if you liked that, you may get a kick out of this

TexAgs91 said:

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The definition of an apple would have seeds built into it. One apple is one apple.

2+2 deals with definitions of mathematical objects, not gravitation. According to their definitions 2+2=4. That's all there is to it.

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The definition of an apple having seeds built into it is an assumption and constraint you've added. It goes back to the room and blue versus azul eggshell with off white trim. Every new detail refines the reality you're describing and reduces the set of possibilities that fit the constraints.

Think of it this way: If I point to a woman in front of you, tell you she has a fertilized egg in her uterus, and ask you how many people are standing in front of you, would you say one or two? If your definition of life is that it begins at conception, it is 2 because that fertilized egg has the potential to grow into a fetus, infant, toddler, and so on. If you think life begins at birth, it is 1. Nothing has changed, but how many people are in front of you can be described differently mathematically depending on the assumptions laid out and the question being asked.

In much the same way, each one of those seeds in the apple is a potential tree that will bear fruit in the form of apples. It's well within the realm of possibility to describe how many apples at any future time t given assumptions on space, water, nutrients, etc and correctly sweet the question, "How many apples am I holding?" because I've never introduced any constraints. The answer is 1 and only 1 as long as you add in constraints like, "...fully developed apples at this exact moment."




2+2, or for a more simple example 1+1, comes with it's own assumptions. 1+1 on its face is simple. It's the easiest math problem imaginable. By mathematical rule it is 2, with the implicit understanding that the ones both describe the same thing being added. The last part is important.

In applied math, 1 describes something. It isn't 1 per se, it is, "1 what?" The "what" is a very important part of the application of the objective 1+1 rule because it determines of the 1+1 rule even applies. If you have different, "whats," then it's more of an x+y situation. After all, x+y can be rewritten as 1x+1y=x+y. Still 1+1, but the solution varies depending on the definition of x and y.


Now think of the square visual example that Carr presents. If we combine the four squares into one, and ask, "How many squares do we have?" the answer CAN be 5 because the outer perimeter forms a fifth square. It didn't have to be, but it can be because it is contained in the set of all possible ways to combine the squares. The answer is 4 if you add constraints such as, "...of the same original size." Even then, adding the squares together in 3 dimensional space to create a cube can produce 6 squares of the same original size. The, "whats," you're adding are very important because they're not just representative of numbers in a set, but objects or complex ideas that can work together beyond the rules of pure math.

DD88 said:

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Snopes Rates Biden's Claim That 2+2=5 As 'Mostly True'

Quote:

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"Sure, Biden got some key details wrong," said Bob Snopes, founder of Snopes. "But the central concept of what he was saying, that two numbers put together make another number, was completely accurate. Sometimes two and two make four. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. It is not easy to become sane."

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2+2=3 only if the IRS gets 25%.

From her own tweet:

"Former mathematician"

I took an advanced math course that consisted of using a slightly altered version of Peano's axioms as a basis to logically prove basic mathematical functions such as addition, subtraction, multiplication, etc. The entire course was constructing mathematical proofs, with help from the professor as needed. About a third of the class dropped out.

It did illustrate how logic provides the foundation for mathematics.

ABATTBQ11 said:

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TexAgs91 said:

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The definition of an apple would have seeds built into it. One apple is one apple.

2+2 deals with definitions of mathematical objects, not gravitation. According to their definitions 2+2=4. That's all there is to it.

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The definition of an apple having seeds built into it is an assumption and constraint you've added. It goes back to the room and blue versus azul eggshell with off white trim. Every new detail refines the reality you're describing and reduces the set of possibilities that fit the constraints.

Think of it this way: If I point to a woman in front of you, tell you she has a fertilized egg in her uterus, and ask you how many people are standing in front of you, would you say one or two? If your definition of life is that it begins at conception, it is 2 because that fertilized egg has the potential to grow into a fetus, infant, toddler, and so on. If you think life begins at birth, it is 1. Nothing has changed, but how many people are in front of you can be described differently mathematically depending on the assumptions laid out and the question being asked.

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You're getting into the specifics of what is being added, which is beyond the scope of the mathematical definitions of 2, + and =. 2+2=4 works just fine. It works when you know you have two of something. And another two of something. It adds to 4. If you aren't sure if you have two of something then hold off on adding until you figure it out.

ABATTBQ11 said:

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In much the same way, each one of those seeds in the apple is a potential tree that will bear fruit in the form of apples....

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More of the same and beyond the scope.

ABATTBQ11 said:

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2+2, or for a more simple example 1+1, comes with it's own assumptions. 1+1 on its face is simple. It's the easiest math problem imaginable. By mathematical rule it is 2, with the implicit understanding that the ones both describe the same thing being added. The last part is important.

In applied math, 1 describes something. It isn't 1 per se, it is, "1 what?" The "what" is a very important part of the application of the objective 1+1 rule because it determines of the 1+1 rule even applies. If you have different, "whats," then it's more of an x+y situation. After all, x+y can be rewritten as 1x+1y=x+y. Still 1+1, but the solution varies depending on the definition of x and y.

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This is good instruction for the user.

ABATTBQ11 said:

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Now think of the square visual example that Carr presents. If we combine the four squares into one, and ask, "How many squares do we have?" the answer CAN be 5 because the outer perimeter forms a fifth square.

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No. Look at your own caveat right above. A large square is not the same as a small square. You cannot mix object types unless you use the tools we have in math such as 1x+1y=x+y.

ABATTBQ11 said:

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The, "whats," you're adding are very important

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Good advice for users of math. 2+2 still equals 4.

If anything Kareem should caution people to be careful in how they apply math. No harm in that. But that's nowhere near the same as questioning if 2+2=4.

Didn't read the whole post...is this about imaginary numbers?

troy_y said:

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Following the responses on twitter is interesting. It is all what ifs, yes but, and philosophical back and forth.

He then presents the following "visual" explanation -

Trying to follow the philosophical oral gratification they are giving themselves - it appears the answer is 1 not 5. The placement of the 4 individual pieces into a single entity is 1 stable form which is the only way he can count the outer box. If one individual piece is removed, then the form will fall and no longer be in existence

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The obvious response is that this is not addition.

It would be a square formation function, given the number n which is the summation of squares from 1^2 up to n^2. The formula for the number squares in a nxn formation = n(n+1)(2n+1)/6

+ is just a symbol for a binary operation just like * is, but most mathematicians don't abuse notation like that. Kareem's operation isn't even a well-defined operation.

This is actually a pretty simple one to tear apart.

It's like saying adding 2 quarters to 2 quarters makes $1.25.

No. It does not. It either makes 4 quarters xor 1 dollar. They are equal.

TexAgs91 said:

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Let's not get bogged down in nonsense like does 2+2=5

Let's get into the good stuff (and yes, this is actually really cool and worth a watch)


And if you liked that, you may get a kick out of this

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Fascinating, Jim!

TexasRebel said:

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This is actually a pretty simple one to tear apart.

It's like saying adding 2 quarters to 2 quarters makes $1.25.

No. It does not. It either makes 4 quarters xor 1 dollar. They are equal.

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Agreed. The whole push for even arguing about 2 + 2 seems to be an agenda for something else.

If there was a real pursuit for describing something new, you wouldn't be trying to champion 'what you know about 2 + 2 is wrong'. There would be a new operator different from + or = used to clearly indicate something other than objective math is going on.

DD88 said:

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troy_y said:

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Following the responses on twitter is interesting. It is all what ifs, yes but, and philosophical back and forth.

He then presents the following "visual" explanation -

Trying to follow the philosophical oral gratification they are giving themselves - it appears the answer is 1 not 5. The placement of the 4 individual pieces into a single entity is 1 stable form which is the only way he can count the outer box. If one individual piece is removed, then the form will fall and no longer be in existence

---

The obvious response is that this is not addition.

It would be a square formation function, given the number n which is the summation of squares from 1^2 up to n^2. The formula for the number squares in a nxn formation = n(n+1)(2n+1)/6

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So is the real day application of this how votes should be counted? That is to say we add the individual votes, then combine them to a pair and add that as an additional vote, then a small group and add that, then a "community" and add that to the overall count? The issue there isn't a math problem, but a geometry problem.

Aggie Joe 93 said:

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TexAgs91 said:

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Let's not get bogged down in nonsense like does 2+2=5

Let's get into the good stuff (and yes, this is actually really cool and worth a watch)


And if you liked that, you may get a kick out of this

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Fascinating, Jim!

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Math is a tool used in physics to model the universe. It doesn't mean that the universe is math. I can make a model of an F-15 but that model is an approximation of the jet, not the actual jet.

Perhaps there are better tools than math to describe how the universe works. We just are so focused on math that we don't look for other, simpler tools. Also, many physicists' egos like the difficult math because it makes them feel superior (I have a degree in physics by the way).

Also, 2+2=5 confuses mathematics and arithmetic. Einstein was a genius in mathematics but horrible at arithmetic.