# Dividing 1 by three proves math is not a universal language

1. Mar 18, 2013

### squawbum

Hello there. I wanted to throw this out there and ask what you think.

I believe that math is a human creation and imperfect and thus cannot be relied on to explain the universe. However the fundamental tool used by theoretical physicists in trying to explain the universe is the human construct known as "mathematics". The only explanation on the reliance on math is because physicists have "faith" in math much like religious people have "faith" in a higher power.

Why do I believe this? Because 1 divided 3 is an human created impossible description of a possible reality. Here is an example. If you take three lines, each measuring 2 feet exactly and combine them into one line, you get a single line measuring 6 feet.

If 6 feet equals 1 Unit, then the result of 1 Unit divided by 3 is an impossible mathmatical description of the actual length because we know for a fact that that single line divided by 3 WILL equal three lines of exact measure.

In one context, the lines are equal and in another they are not. This is a mathmatical paradox and proves that math is actually relative to human perception and perspective. This being the case, how can we have such "faith" that the conclusions of theoretical physicists are correct? For example, negative energy must exist because we have positive energy to "balance" the equation? That might be right in theory but is it right in reality?

Am I just full of it here or are these legitimate concerns?

Take care.

2. Mar 19, 2013

### SteamKing

Staff Emeritus
What you are saying is not right, it's not even wrong.

3. Mar 19, 2013

### micromass

Staff Emeritus
We have been able to send a man to the moon and to send an object out of the solar system. So we must be doing something right...

No, scientists don't accept math blindly. We use math to make models and then we perform experiments to test the models!! If those experiments show that the models are wrong, then we reject the models and the math.

4. Mar 19, 2013

### nidefatt

Friend, your concerns are valid. Math is always about perspective. What we call "problems" or "solutions" are only such from our perspective. Every formula is a perfect description. It's only our needs that require us to redefine it.

Still, you must realize that your bigger point is wrong. Mathematics is incredible because it describes our universe at the most fundamental level. Perspective may change what "solution" you want, but it can't change the fact that a particular formula is true or false. Love math. It is salvation. :p

5. Mar 19, 2013

### uperkurk

Math is unlike anything else we know. You can take 1 and 1 and you'll get 2, you can do this calculation an infinite number of times and you'll always get 2.

As maths gets more advanced, the rules still apply. People come up with theories, then they test them over and over using experiments which in turn prove that the equation is correct.

Find me a circle who's ratio of circumference to its diameter is not 3.14159... We can say that with absolute certainty, no matter how large or small the circle we will get the same answer.

I believe that no intelligent life can exist without mathematics. So it is absolutely unquestionable to say that mathematics is not the universal language, although of course different races will use different notation and completely different equations.

But nonetheless they're going to get the exact same answers to us. As for the very advanced maths and physics that exist such as E=mc² we could be wrong, but so far every single experiment we've done has obided by this law so I'm willing to bet that E=mc² is just as solid as 1+1=2

6. Mar 19, 2013

### georgir

I don't get it. In what context are they not equal?
If you are referring to the fact that 1/3 has no exact decimal representation, you did not state that clearly enough (or at all). Also, that is just related to the decimal numbering system and is no paradox. 1/3 is a specific exact number regardless of if it has or has not an exact representation in some numbering system. BTW, it has an exact representation in trinary numbering system for example, but again, that is completely irrelevant. For another example, the length of the diagonal of a square with a side 1 may not have an exact representation in any numbering system, and it still is a well-defined, specific, non-ambigous, non-paradoxical no-nonsense number.

7. Mar 19, 2013

### mikeph

For someone who is dismissive about mathematical rigour, you throw the word "prove" around very lightly.

1/3 is an exact number just like 1 is. Your three lines are exactly equal in every context.

I think these confusions are more likely a result of a misunderstanding on your part than a fundamental error in logic.

8. Mar 19, 2013

### Crazymechanic

I think the OP is asking a more fundamental and philosophical question just the way he made the question and the analogy is kind of strange and not a very well performed argument to use to explain this more fundamental property of the universe.

I think the question would be does nature knows mathematics herself when she does and makes all the things we see and try to understand.Or if someone who believes in a divine deity one can ask does the creator of the universe knows mathematics ...

If you ask me personally I think that mathematics is valid and useful but NOT PERFECT.
It is a human made construct to understand the things that we haven't made that are just there like even ourselves.When a baby is born does the birth involves mathematics? Does our own brain functions based on mathematics? Or rather we grown up and suddenly want to understand who we are and then we use the best way of describing ourselves and the world around us and somehow it happens to be that for the majority of people who explore the world (scientists) it happens to be mathematics.But numbers are only useful for someone who knows the human made meaning behind them.I can show a equation to my cat and he would not give a **** about it and yet that doesn't make him any less capable of doing what he does.Being a cat.Scratching doors and even learning how to open the fridge to get food.He just learns the way that suits him best.like we do.
But remember math is only good for the things we can "see" or measure and encounter , math is useless for all the phenomena that we haven't either seen or are unable to like distant galaxies receding from us faster than the speed of light or before the big bang or if you prefer the start of the universe as we know it.And many more these all are limiting factors to what we can know.
Mathematics is not wrong for what it does , explain to our human conscious intellect the things the way we can understand them.But It's not a "GOD" in a sense that some say it is universal or the same everywhere and to everyone.

A great artist (painter or so) a theoretical physicist and a child , they all have their understanding of the universe around them and all three of them have their own way of exploring the universe around them ,a physicist calculates the exact height of a Christmas tree , a child says that the tree is high and an artist says that the tree is small because his painting includes the whole city in the background now is there someone who can tell me which one is right or which one is wrong? None of them are right and none of them are wrong, they are each right in their own frame of reference , rather each of them uses the way more acceptable and understandable to them to make the one thing common to everyone- exploration and understanding.

Mathematics is like a car if you don't have the fuel for it it's useless ,the fuel being the meaning behind the otherwise random black colored stripes on a piece of paper or wall that we call numbers and digits.

Last edited: Mar 19, 2013
9. Mar 19, 2013

### the_emi_guy

I received the book "What is Mathematics Really" as a gift several years ago, it was interesting and touched on the very ideas you are pondering.

Here is the link to the book review from the American Mathematical Society.
www.ams.org/notices/199909/rev-dubinsky.pdf

This may be of interest to you if you want to study this aspect of the philosophy of mathematics.

As crazymechanic said, your question is valid even though your specific example makes no sense.

10. Mar 19, 2013

### ZapperZ

Staff Emeritus
11. Mar 19, 2013

### Jimmy Snyder

In my opinion, faith in science is misplaced. However, the fact that some scientists have faith doesn't mean that science is religion. The fact that some religious people lack faith doesn't mean that religion is science.

12. Mar 19, 2013

### Jobrag

"I believe that math is a human creation and imperfect and thus cannot be relied on to explain the universe."

What prevents perfection in a human creation?
I don't think that maths tries to explain the universe what scientists use maths for is to describe the universe, explanations are for philosophers.

13. Mar 19, 2013

### Crazymechanic

@Jobrag it's not like I can agree with you fully.
Explanations are not only for philosophers they are also for physicists and for actually everyone who tries to understand something no matter what the field.
Even churches use pastors to explain the bible to those who can't understand a bit.
A child uses his mothers explanations to understand why he burnt his fingers on a hot cup of tea.
If we would leave explanations only for philosophers it would be hard for us to ever start doing science in the first place , because what's the use of doing something without the search for explanation and meaning behind it and if we find there is none then that becomes the explanation and meaning in that given case.

As to what prevents perfection in human creation , first of all humans themselves.Only when we will have a machine that will be fully capable of doing the necessary maintenance and all the work automatically then we will be able to say that we can leave out the operator error but still we ca t get rid of things like wear and possible outside effects on the system.
Things like these tend to render everything we make no matter how advanced imperfect.
The other factor would be that we are fundamentally limited to our knowledge and dimensions in which we are , and our knowledge is not full if there even is one.So unless you know every single bit of he puzzle you cannot claim to have solved it.
I agree that making a perfectly good car doesn't involve understanding black holes at distant galaxies nor it affects it any way but then again a car is just a car and with higher level of knowledge who knows what better means of transportation we could engineer.

14. Mar 19, 2013

### leroyjenkens

You caused that problem by changing the units. You changed the 6 feet into 1 "unit", and then divided by a unitless quantity. If you kept it in feet, then dividing by 3 would tell you the length of each of the lines; 2 feet. But instead, you defined 6 feet as 1 "unit", which when divided by 3 will give you 0.333... in the unit of "units", not feet. Each of the lines will be 0.333... "units."

15. Mar 19, 2013

### PuckNorris

By dividing 1 by 3 you get 1/3 which is EXACTLY one of the three lines with equal mesure. If you are talking about the decimal representation:

$0.3333\ldots = \lim_{n\to\infty}0.\underbrace{ 33\ldots3 }_{n} = \lim_{n\to\infty}\sum_{k = 1}^n\frac{3}{10^k} = \lim_{n\to\infty}\left(\frac{1}{3}-\frac{1}{3}\times\frac{1}{10^n}\right) =\frac{1}{3}-\frac{1}{3}\lim_{n\to\infty}\frac{1}{10^n} = \frac{1}{3}.\,$

There is no paradox at all. You can change the units to whatever you like and the math won't break. Of course there are units that are easier to use like meters for example instead of feet, inches, yards, miles and what not.

16. Mar 19, 2013

### Staff: Mentor

Why is perfection even required? Again, we put people on the moon without it.

17. Mar 19, 2013

### PuckNorris

I've never seen any philosopher to actualy explain anything that is connected to reality and his explanation to be actualy true.

Believe it or not mathematics even if possibly not perfect is the best description we have. It have been shown that math works way better for describing the universe than our human language. Trying to explain physics with only our natural language without any math which is common practice in popular science(books, tv shows) most of the time causes a lot of confusion because it cannot be accurately represented.
When we were evolving our language was used mainly to communicate with other people for daily tasks which we needed to do in order to survive. It is not made for explaining the laws of nature.

18. Mar 19, 2013

### Ryan_m_b

Staff Emeritus
"Perfection" is a nonsense term here. Perfection describes a system/object that is the best possible configuration/design for the context being discussed. Without context the whole notion of perfection is useless. And why can't humans define a context and then invent a perfect solution?
Absolute rubbish. Faith is belief without or inspite of evidence. Mathematics can be shown to work via mathematical proof and in application by getting the job done. Just like everything in science.
You're just playing a word game of units here. It's not impossible to have 0.333.... of an object, it might be impossible to write that number down in full because it is infinite but that doesn't mean a thing. If I'm in a group of three people when I am 0.333.... of that group and I exist. Whether you use "0.333..." or "33.333...%" or "[inert any symbol here]" doesn't matter, this is just a symbolic expression of one third
It's not the case and with all sciences we demonstrate that something is correct through experimentation or mathematical proof. Science doesn't work in a bubble creating mathematical descriptions of the universe, it goes out into that universes and uses observations to create a model (not always involving maths at anything but a superficial level) that it then tests against that universe to measure it's validity. The use of the word "faith" here is entirely unwarranted.
I don't know if the rationale behind negative energy is because we have positive energy (any physicists want to jump in here) but comparing our models to reality is exactly what science does.
Your conclusions are based on false understanding. If you'd class that as full of it then I suppose you are.

19. Mar 19, 2013

### Ryan_m_b

Staff Emeritus
Err mathematical symbols are an example of human constructed language. 1 + 1 = 2 is equivalent to if I have one of this and one of this I have two. All our language is a set of symbols that attempt to transfer concepts from one mind to another via shared consensus and analogy. The former means that for most people symbol X means the same thing and the latter means that when a novel concept is trying to be transferred the symbols used are analogised to ones that have consensus.

Maths might be a "universal language" in the fact that no matter where you are the concepts that our symbols represent will be the same but that's not necessarily unique to maths and it isn't true of maths in terms of the symbols we use.
Do you mean language or ability to use language? Those are very different things. Are ability to use language is determined by a number of physical faculties like our ability to model concepts in our mind, our theory of mind for others, our ability to remember certain patterns of behaviour and assign them to symbols etc. Our languages in the sense of the written, verbal and physical symbols we use to convey concepts can be as complex as our ability allows and can even help us discuss things that we cannot conceive of directly.

For example: we can't conceive of 4 dimensional shapes directly but we can create language to describe the characteristics of said shapes for meaningful applications. (This example might be a bit weak so if anyone has a better one please throw it out).

20. Mar 19, 2013

### Tosh5457

Math itself can't be wrong, unless you want to argue logics is wrong. Math uses a set of axioms to start the reasoning and aristotelian logic to develop them, nothing more. It only uses logic rules, it doesn't make any assertion about reality. The only wrong thing that could be done is to apply a mathematical model to a real problem. There are many cases of this in many disciplines, but in Physics the models are pretty accurate and able to explain everything as well as making correct predictions. So what's your concern?