Why mathematics is neither absolutely nor objectively "right."

[steve_bank]

I'm wondering how you can be an engineer with such poor writing skills.

Have you looked at his profile? maybe the problem is your reading skills or lack thereof.

Are profiles somehow absolutely true while posts are not? The way I see, there can be as many lies in a profile as there are lies anywhere else.

I am a liar. What I say is absolutely true.

 

[Cheerful Charlie]

Unfortunately for me I have diabetic retinopathay, my eyesight is poor. Glasses and large text helps, I don't always catch the underline for the spell checker.

Do you have some adaptive equipment you use to do your engineering work? I'm wondering how you can be an engineer with such poor writing skills.

Math arose out of practical necessity. Counting.

I've studied the history of mathematics, and according to what I've read, the earliest math involved time reckoning, in particular the calendar.

If I put 2 potatoes and two onions in a pile how many total objects are there? Can there not be 4 objects?

Yes, that's what we're taught to call that quantity. However, depending on the "objects" being summed, the result can be something other than 4. For example, if you add 2 clouds to 2 clouds, how many clouds do you have? You could have only one cloud! Or 2 or 3 or any number of clouds. So nature cares little for our inventions, and math like any invention does not always "work" the way we intend.

You are conflating some kind of philosophizing with objective math.

There is no "objective math," and it's very suspicious that any engineer would think so. The mathematics I've been citing on this thread, which you appear to be completely ignorant of, is known as modular arithmetic. As a reference, I'm using Linear Algebra: A Modern Introduction 3rd Edition by David Poole, pages 13-14. So the math I'm using is math that is standard and commonly accepted by mathematicians.

My point on Boolean Algebra is that logic and objective mathematical truth is not just the purview of math and philosophy, it is everywhere. Global commence and the jet you fly on depend on math to be absolutely true.

What you're saying here is a non sequitur. It doesn't follow that if math can be used to model things in the real world, then math must be absolutely true. Commerce and airplanes don't rely on what is absolutely true but rely on what is true enough.

A philosophical thought experiment.

You go into a store and pick up 3 objects to buy. You go to the checkout and yio are charged for 4 objects. You protest and the cashier says '1 plus 1 plus 1 is not always 3, sometimes it is 4".

Would yiu apy for 4 objects?

No, I wouldn't pay for what I didn't intend to buy. Stores as far as I know don't use modal arithmetic to charge for items, so 3 items are not 4 items.

But let's go with your analogy, and say you're looking for gala apples in that store. You see none on the shelves, and you ask when the gala apples will be in stock. The clerk apologizes and explains that the gala apples won't be in stock for another two hours. You look at the time and see that it's 11 o'clock Do you conclude that the apples will be in stock at 13 o'clock?

Hint: Use modal arithmetic!

13! Military time. It is unambigous. 12:00 might mean Midnight or Noon. And in the distant past, there was no hour as we understand it.

 

[steve_bank]

But let's go with your analogy, and say you're looking for gala apples in that store. You see none on the shelves, and you ask when the gala apples will be in stock. The clerk apologizes and explains that the gala apples won't be in stock for another two hours. You look at the time and see that it's 11 o'clock Do you conclude that the apples will be in stock at 13 o'clock?

It depends, as Charlie said, on a twelve hour or 24 hour clock,

I think 13 0'clock is semantically incorrect There is no 13 'o'clock'.

With a 24 hour clock it is usually 13 hundred hundred hours.

Have bo idea what you are inferring by modulo arithmetic. Modulo arithmetic is commonly used in software for different things. If the link is what you are referring to write aa modulo arithmetic that demonstrates what you mean by your clock example.

There is an old saying, a little bit of knowledge is dangerous.

What is modular arithmetic? (article) | Khan Academy

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

www.khanacademy.org

Modulus arithmetic does not mean arithmetically 3 can equal 4, you are probably misusing and misinterpreting modulo arithmetic.

Modulo aritmetc is a definition within math, and does not equaye to regular arithmetic.

 

[Jarhyn]

2+2=4. This is true. No matter what modulus you choose, what notation you use.
Binary, decimal, hexidecimal, octal. Roman numerals, Arabic numerals or Aztec numerals. Anything else does not work in real world operations. If you want a deeper understanding of this, we have the Peano axioms, Cantor's set theory. Russell and Whitehead, Frege and others to explain to you why this works. Underlying mathematics is logic.

2+2=0 is true in unsigned integer math on the 2 bit unsigned ring.

2+2=-4 in 2's compliment signed integer notation on 3 bits with "MSB" denoting sign, just as 2+1=3, and 2+3=-2, and 2+2+2+2=0.

It depends a lot on how the system being observed functions.

Of course underlying this is logic, undeniably. This is an application of set theory.

But 2+2=4 exactly when that's the result of the operation, and at no other time.

 

[steve_bank]

I wish we went to a 24 hour clock.

Then I would not have to worry whether it is am or pm.

I think I am starting to see Soldier's problem.

He does not know enough to distinguish between equality andthe equal sign between arithmetic and counting, and oter forms of math.

4 mod 3 = 1 is derived from a non arithmetic definition of modulo arithmetic.

So, I cann see how he can conclude 2 + 2 does not always equal 4 based on skimming through pages on the net. Hence his assertion that math is not absolute truth.

 

[Elixir]

2+2=4
if you have two jugs of water that hold 2 Gallons each you have 4 gallons of water.
Pour them both into a five gallon bucket and you STILL have 4 gallons of water.

It doesn’t apply for adding clouds simply because “a cloud” is not a quantum. Additive math doesn’t apply and semantic games don’t negate the fact that 2+2=4.

 

[Swammerdami]

Oh my. Qhaavat-Xehtre rssrpg and all that!

I do ask budding "mathematicians" to address Puzzle #3 in the following thread. That will be too easy for the best of you; try #4.

Pecking Orders and "pecking games"

Recently I mentioned a "pecking order" in another thread. The Rock < Paper < Scissors (< Rock) game is an example of such a 3-cycle in a pecking-order graph. A famous military analog is pikemen > horse_riders > archers > pikemen which becomes light_infantry > motorized_infantry > artillery >...

iidb.org

 

[bilby]

13! Military time. It is unambigous. 12:00 might mean Midnight or Noon

Only Americans call 24 hour clock times "military".

And I work with runs that use continuous daily time. So an eight hour shift starting at 16:15 on January 5th finishes at 24:15 on January 5th, and six hours after 22:23 is 28:23 on the same date.

This is a legacy of the weakness of 1970s computers. Subtract start time from finish time giving total time, which works great in COBOL, but leads to employees getting paid negative wages, unless you ensure that finish time is always greater than start time.

 

[Cheerful Charlie]

It is sobering to realize standardized time only started in the late 1800's to accomodate train schedules.

 

[bilby]

It is sobering to realize standardized time only started in the late 1800's to accomodate train schedules.

Not really. It's origins are two centuries earlier than that; It was the railways that brought standardised time to the masses, starting in 1847 with the adoption of GMT by the Railways Clearing House in the UK; but maritime navigators had been using Greenwich Mean Time since Nevil Maskelyne's 1767 Nautical Almanac, and astronomers had been using Mean Time since John Flamsteed's conversion formulas (used to calculate Mean Time from local Solar Time), were published in the 1670s.

Of course, railway time rapidly expanded beyond the railways, and became the standard for factories, offices, and other workplaces, making it unavoidable to most citizens, but that process didn't really finish in the UK until well into the twentieth century, and took even longer in many other countries.

 

[Unknown Soldier]

But let's go with your analogy, and say you're looking for gala apples in that store. You see none on the shelves, and you ask when the gala apples will be in stock. The clerk apologizes and explains that the gala apples won't be in stock for another two hours. You look at the time and see that it's 11 o'clock Do you conclude that the apples will be in stock at 13 o'clock?

It depends, as Charlie said, on a twelve hour or 24 hour clock,

I think 13 0'clock is semantically incorrect There is no 13 'o'clock'.

With a 24 hour clock it is usually 13 hundred hundred hours.

Have bo idea what you are inferring by modulo arithmetic. Modulo arithmetic is commonly used in software for different things. If the link is what you are referring to write aa modulo arithmetic that demonstrates what you mean by your clock example.

There is an old saying, a little bit of knowledge is dangerous.

What is modular arithmetic? (article) | Khan Academy

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

www.khanacademy.org

Modulus arithmetic does not mean arithmetically 3 can equal 4, you are probably misusing and misinterpreting modulo arithmetic.

Modulo aritmetc is a definition within math, and does not equaye to regular arithmetic.

Steve, I think I'm going to rest my case. I've tried my best to explain my position to you on this issue, but you don't seem to be getting it.

 

[Elixir]

you don't seem to be getting it.

Neither is anyone else. But buying it would be more accurate.
What you are doing is tantamount to picking up a whole series of wrong size wrenches, pointing out that they don't always or even mostly work, and announcing proof that the whole concept of transmission re-builds is bogus and they charge too much.

 

[steve_bank]

But let's go with your analogy, and say you're looking for gala apples in that store. You see none on the shelves, and you ask when the gala apples will be in stock. The clerk apologizes and explains that the gala apples won't be in stock for another two hours. You look at the time and see that it's 11 o'clock Do you conclude that the apples will be in stock at 13 o'clock?

It depends, as Charlie said, on a twelve hour or 24 hour clock,

I think 13 0'clock is semantically incorrect There is no 13 'o'clock'.

With a 24 hour clock it is usually 13 hundred hundred hours.

Have bo idea what you are inferring by modulo arithmetic. Modulo arithmetic is commonly used in software for different things. If the link is what you are referring to write aa modulo arithmetic that demonstrates what you mean by your clock example.

There is an old saying, a little bit of knowledge is dangerous.

What is modular arithmetic? (article) | Khan Academy

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

www.khanacademy.org

Modulus arithmetic does not mean arithmetically 3 can equal 4, you are probably misusing and misinterpreting modulo arithmetic.

Modulo aritmetc is a definition within math, and does not equaye to regular arithmetic.

Steve, I think I'm going to rest my case. I've tried my best to explain my position to you on this issue, but you don't seem to be getting it.

Again post an equation or mathematical function that makes your point. The onus is on you to post your proof, not on me to read a link. If ypu can not do that yiu have no credibility. Any yea-who can post links.

The problem for you is I have used modulo arithmetic, as well as most of general applied math. Most of us electrical engineers are applied mathematicians.

Do me a favor. If you ever work on a bridge design let me know so I can avoid it.

 

[Elixir]

Again post an equation or mathematical function that makes your point.

I believe U.S. thinks that the fact that there are limits to applied mathematics - like trying to add clouds as quanta - makes his "point" that 2+2≠4.

If you ever work on a bridge design let me know so I can avoid it.

If you need one made of water vapor, he's your guy!

 

[steve_bank]

On occasion one needs to now if a number is odd or even.

A code snippet using modulo arithmetic. Scilab script. All or most computer languages support modulo arithmetic.

x = 13

if(modulo(x,2) == 1) then disp(x, " ODD")
else disp(x," EVEN")
end

or C++ where % is the modulo operator.

int x = 13;

if(x%2 == 0) cout<<"EVEN"<<endl;
else cout<<"ODD"<<endl;

Soldier, I will leave it here.

 

[Unknown Soldier]

you don't seem to be getting it.

Neither is anyone else. But buying it would be more accurate.

If you don't learn the material, then how are you ever going to know the difference?

What you are doing is tantamount to picking up a whole series of wrong size wrenches, pointing out that they don't always or even mostly work, and announcing proof that the whole concept of transmission re-builds is bogus and they charge too much.

Well, maybe rebuilding transmissions is "bogus" and it should come as no surprise that most people think the charge is too high. To find out, it makes sense to investigate the matter to see where the truth is. Have you checked the math behind modular arithmetic to see if I'm correct in what I posted about it? If you do so, then you'll know whether I'm right or wrong.

 

[Elixir]

Have you checked the math behind modular arithmetic to see if I'm correct in what I posted about it?

Are you a parrot?
Modular math was explained to you.
Now you’re just NWRT.
Buh-bye.

 

[Emily Lake]

It's very popular these days to see mathematics as one truth we can know is objectively and absolutely right. I must disagree. A common example of this supposed absolute and objective truth is the equation 2 + 2 = 4. We are told that for all times and places, 2 + 2 = 4, no matter what! If human beings went extinct, then 2 + 2 = 4 still holds as true. If the dinosaurs had the brains, then they would have known 2 + 2 = 4. If there's an advanced civilization of extraterrestrials in the Andromeda galaxy, then they know 2 + 2 = 4.

It's not true that 2 + 2 is absolutely 4. Depending on the rules mathematicians are using, 2 + 2 = 0 might be the case. In modular arithmetic, 2 + 2 might not even be defined at all much less true. For example, in binary there is no 2.

So the truth of 2 + 2 = 4 depends on what arbitrary set of rules you are using. No absolute or objective truth can be so arbitrary. Hence in general, mathematics is neither absolutely nor objectively "right."

You're not even wrong here.

And you clearly have no understanding of how modular mathematics work. Regardless of the modulo of your system, and regardless of the terms you use for your numbers... the relationships ALWAYS hold.

 

[Emily Lake]

As I see it, it's always important to understand the underlying reasoning behind any discipline, mathematics included. Most people at best skim the surface of mathematics learning only techniques. Without the knowledge of the logic behind mathematics, you'll be hard-pressed to develop new mathematical techniques or prove that those techniques are reliably applicable. Do you really think that mathematicians never bothered to prove the math behind relativity?

I'm guessing you're in that camp yourself. Maybe ponder that a moment.

 

[Emily Lake]

In that case you agree with me that 2 + 2 is not always 4.

This is demonstrably false. No matter what nomenclature, or what modulo, it is ALWAYS true that...

Bob has
Sue has

Together, Bob and Sue have