Are there any Flaws in Math?

Cmdr paddy I understand what you're saying, but I we just see things differently.

I just can't perceive math as valid or absolute, when it's fundamentals were created by a guess of wild estimation.

To me, math is based on someone at some point holding up their finger and agreeing that such a distance was an inch or that a mutiple of objects were named as number to categorize the clutter.

Without a solid foundation; such as an inch being equilvalent to the distance between stable strings or particles in a substained manner, math cannot be perceived as valid.

Technically math only works because it allows our guesses to be vast; but when you require a more absolute knowledge, math falls apart. Thus this is why quantum mechanics does not mesh well with general physics.

The best way I can explain is :

An inch is valid in modern equations only because the room for error on the quantum level is so vast. In such a level this inch is almost infinite in size, thus our miscalculations bare no real effect; however when such calculations are applied on a quantum level the room for error is non existent and thus without a constant defined structure of measurement or reasoning to apply on the quantum level, this level of reality will continue to elude us.

You math is merely an index, an attempt to bring order to the choas. To a point it has served it's purpose, but in order for us to move foward; someone will have to take the crayons away from mathematicians and stop letting them eat them. We have to move foward in adolescence and rationalize, we must create a proper index and learn how to properly index before we can truly understand that we don't understand.

Once we reach this point; we will hopefully begin to understand there isn't any real order to the chaos. We only perceive this supposed order.

As for someone approaching to inform me that I do not exist; I would simply smile and agree. In reality I don't exist unless I chose to exist; thus I don't really exist. My perception of being is far from reality; in my mind only is my existance apparent; in the reality I am nothing short of strings traversing randomly.

Humans are funny that way.

Originally posted by hanburu_juuboku
I just can't perceive math as valid or absolute, when it's fundamentals were created by a guess of wild estimation.

To me, math is based on someone at some point holding up their finger and agreeing that such a distance was an inch or that a mutiple of objects were named as number to categorize the clutter.

I can't perceive measurement units as a part of math. Units of distance, weight, heat, force etc are just human convention that don't have a relation to mathematics at all.

But if someone holds up their finger and says "how many fingers am I holding up?" and the answer presented is two, and not one, and then the counter attempts to prove it, then that's math. Flawed math.

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Math is an abstract concept. Independent of reality.

measurements are attempts to apply mathamatical principles to the real world.

In math there is no scale of measurement.

The number 'one' can be bigger than an infinite number of Universes or smaller than the tiniest portion of a quark and still be exactly the same concept.

Sort of like algebra, one is simply a symbolic concept. In its realm of the imagination it is perfect, whole and discrete. Inexactness happens when we attemp to apply it.

The amazing thing is that math principles do work, with varying degrees of success in reality.
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Couldn't have put it better MaskedAvatar. Mathematics is not about lengths or measurements it is about numbers, whatever they may be. People have let numbers stand for quantities because they are easier to comprehend and it is easier to make examples of questions where there are (supposedly) real tanglible things involved, not some airy-fairy idea of 'numbers'. Most advanced mathematics has so little to do with the numbers themselves and so much to do with their properties and how we can manipulate them that to some it doesn't seem like mathmatics at all.

In fact some mathematics is far closer to philosophy than you'd think, the idea of limits and things approaching infinity are just as much philosophical questions as mathematical questions, at least i think they are

[edit on 21/4/05 by cmdrpaddy]

What has always bothered me is that 0! = 1

I have no idea how that works, and yet that is the basis for Taylor and Maclauren series which are the basis of things like low angle approximations for pendulums using the modified newton's second law equation, T=2*pi*sqrt(L/g) where L is the length of the string the pendulum is on and g is gravity. However oddly enough, that equation works. So 0! must equal 1....

Anyone here a study math in college? I am an Electrical Engineer so I have to take a million math courses anyways, but my courses are more applied than theory, I'm sure a math PHD could straighten this out for us.

[edit on 4/21/2005 by lockheed]

It would take less than a maths phd to help you.

Basically its about the gamma function, only for integers. It has the property of being the factorial function if you only use integers with it, when you play around with it a bit you see that 0! is in fact 1.

Link to Maths World article on the Gamma function

So-called "imaginary" numbers (I, too, think they should have been called something else) are quite real, and occur in the real world in several places (for example, the electrical current running through circuits with capacitors and inductors; the force on a mass-loaded spring; and so on). The real and imaginary numbers form a union of numbers called the complex numbers. Like everything in Mathematics and Science, the concepts were discovered, not invented. (You can't 'invent' the concept that 2+2 = 4; it was always there, you just discovered its existence.)

Concepts in Mathematics and Science are abstract and concrete; they can be proven, and reproduced on demand. Some of these posts asking "Is Math flawed?" appear to come from the perspective of a liberal arts person trying to understand the abstract and concrete. A concept in Mathematics or Science isn't correct becuase someone decided it was correct; it's correct because it is simply true, a fact. Impressions, interpretations, and opinions are fine in liberal arts fields such as Literature, Art, History, and Government, but in the fields of Mathematics and Science, they are useless. What some are perceiving as 'flaws' in Mathematics are in fact gaps in our overall knowledge, that will be filled over time as new discoveries are made.

Pi = 3.14... is the ratio of a circle's diameter to its circumference; no matter how small or large a circle is, if you divide the diameter of the circle by the circumference of the circle, you will always get Pi.

As to the question of units of measurement -- it's true that the units we use to measure dimensions of our physical world are human conventions, but the dimensional analysis of the physical world is pure Mathematics, and remains true no matter what units of measurements you use.

The answer to questions such as "Why does 0.9999... = 1?" and "Why does 0! = 1?", and much more, can be found at Dr. Math's website. Check it out!
mathforum.org...

ive herd of flaws in math but i have never seen facts to prove it. as far as the square root of negative seven its about:
2+(-3^-2) or 2+ the square root of 3i.
the square root of -1=i. you cant square a negative number without "i."
straight lines are mathamatic equations because no one can draw a staight line. thats my best answer for this after six rum&cokes and a 40oz. of Old English 800.

the problem with math isn't really its accuracy. Its its complexity. Math is supposed to be simple and elegant. Its supposed to be the one part of the universe we can decipher.

But its not simple or elegant. It takes 200 some odd pages in the principia mathematica to prove 1+1 = 2. What's simple about that?

The problem with repeating decimals is and old one and the problem with it is perplexing.

Goedel worked on something like this called the "incompleteness theorem" which says some maths just cant be solved and proven. It may be the perfect right answer but you could never solve it completely. It drove him to madness (or in his case maybe made it worse). . .

there are also a couple other mathematical theories that also have driven people into madness. . . math is deep and confusing but don't let it bother you

Google Video Link

[edit on 17-7-2009 by constantwonder]

I can never get my head around how .999~ is equal to 1 no matter how it has been explained to me... but then again the concept of infinity is also mind boggling...

Math does seem to be rather perfect... the only down side or possible flaw to math is that it is abstract and some of it seems to me to be only demonstrated on paper.

Here are some deep thoughts about math/science/the universe...

... math as humans have portrayed must only be a limited theoretical tool and it cannot be an exact picture of the universe... my reasoning: There appears to be no such thing as any even two identical things in all of existence... therefore we can only ever really have one of any real defined thing... furthermore... the quantity zero cannot exist... if zero equals nothing and there is always something then zero cannot exist... the only way zero exists is in relation to a given context... ie. John has no (zero) apples and Sue has an apple... the zero only relates to the given context ie. John in this example... infinity also seems to be an unprovable concept... it would appear then that math as dynamic and perfect as it is and as useful as it can be... is only a "picture perfect" representation of the universe... and it would appear in fact the real way the universe is made up is more mysterious than we know and some how evades and exceeds the limitations of mathematics... further more it would seem that is impossible to divide anything exactly into a fraction... ie if you cut a piece of pie in half one half will always be slightly larger than the other... no exact fractions or measurements as our instruments would always be too crude... negative number systems... when do we ever have a negative of anything... John cannot be minus one apple... he either posses none or has one or "more"... don't get me wrong... math is a very important and useful field of study and has many real life applications especially in computer technology and the engineering of all that we have ever invented, made or built... but none the less though it appears to work perfectly on paper over and over again yet it would seem that what is going on in the universe is some how at least slightly different...
...there are also postulations made by math and science that are truly only 'theorectical' in nature but are often accepted and officially deemed as fact... I say "theorectical" because they cannot or have not been duplicated once let alone repeatedly in the real world... ie the concept of creation of any kind and of evolution can only be considered postulations as no one has of yet been able to duplicate the process... there are probably other examples... life is truly a mystery... and what ever we purpose requires elements of guess work, estimation and faith in our own conclusions.

Originally posted by The_Final
I wonder if there are any flaws to math?

How about this: 3 guys go to a motel, the manager says 30$ for a room, the 3 guys each pich in 10$ = 30$.
the manager as some remorce about the price he charged, so he sends the bell boy the give back 5$, so that they paid 25$ for the room.

On his way to give back 5$, the bell boy says to him self 3 guys 5$ is hard to divide, so he pockets 2$ and gives
each of the 3 guys 1$ back. so that they each paid 9$.

3x9 = 27$ plus the 2$ pocketed = 29$.... where is the other $

I don't know if someone's already said this, but 0! = 1 is a flaw in my opinion. It's made to equal that to make some other stuff work, but there's no logic behind it.

Originally posted by The_Final
I wonder if there are any flaws to math?

How about this: 3 guys go to a motel, the manager says 30$ for a room, the 3 guys each pich in 10$ = 30$.
the manager as some remorce about the price he charged, so he sends the bell boy the give back 5$, so that they paid 25$ for the room.

On his way to give back 5$, the bell boy says to him self 3 guys 5$ is hard to divide, so he pockets 2$ and gives
each of the 3 guys 1$ back. so that they each paid 9$.

3x9 = 27$ plus the 2$ pocketed = 29$.... where is the other $

Manager has 25
Boy has 2
Men have 3

So they payed what the manager has + what the boy has= 25 + 2 = 27

They themselves have 3.

27 + 3 = 30

I'll let you know once I solve "P versus NP"

en.wikipedia.org...

Nearly all the math you get in high schoold and as an undergrad is perfect. There are flawed math theories, but you won't be exposed to them until your senior year in college, and then only if you are a math major.

I once had a math prof who was writing a book about the "set of all sets". Years later, I discovered that "set of all sets" is an oxymoron.

There is a branch of math called "constructive math", in which infinities do no exist. If you can't construct a math entity from integers in a finite number of steps, it doesn't exist. What's true in math generally ain't necessarily true in constructive math.

Chaos theory is an infant branch of math. Hardly anything is known about chaos.

Another infant branch of math is string theory, which pretends to be physics, but is really only about numbers.

reply to post by The_Final


Making use of infinite's and renormalization is a huge math flaw that is in common scientific practice.

Using such devices, a person can essentially prove that 1 = 2.

This method of calculation is used heavily in Astrophysics and Quantum Physics. It's what they use to "prove" ridiculous things like Black Holes and Dark Matter. Things that have never been proven to exist by direct observation.

math is infallable, but our understanding, as well as our calculation of it, is not.


and while imaginary numbers are called such, they are very necessary and very real; they just aren't numbers that we can visualize. They exist all around us however, in everything, especially quantum mechanics, fractals (found everywhere in nature from big to small), codes, etc.

reply to post by cmdrpaddy


I think this is one of the most remarkable properties about mathematics. We have to assume that every electron behaves exactly the same way throughout all of space and time in order to reason about distant phenomena. However, with math, we do not need to assume, but we can know that the foundations of math are consistent throughout space, time, and even other universes.

We can assume that aliens capable of interstellar communication would know about prime numbers for example, because they are universal given the successor definition. If aliens count, they will know about prime numbers.

But what if they don't count? Well, in that case, i think they truly are alien.

I think the answer to the OP's real question is "no, with a 'but'...." Math is an abstract system of reasoning that is internally consistent and can be used to make meaningful descriptions of what we'll call "the real world." There are no flaws in the math you are learning in school, so memorize those multiplication tables. The internal logic of math sometimes requires concepts that have no apparent analog in our experience of "the real world"; irrational and imaginary numbers, multiple dimensions and so forth. As has been pointed out, there are sometimes flawed theorems or lines of reasoning in more advanced mathematical research; don't worry about them until grad school. Mathematics is notoriously incomplete; Euclidean geometry was inadequate for describing the geometry of Einstein's space-time, fortunately some Russian mathematicians had been fooling around with some alternatives. String theory has proven to be a difficult nut to crack, although perhaps some day someone will come up with a new branch of mathematics that can describe it accurately and elegantly. (Aside: no, I'm just not buying determining the Yalu shape configurations through trial and error!)

reply to post by The_Final


There is one Mystery for me in Nature that I would like to confirm to be Absolute , the Mathamatical Geometry behind the Mandelbrot Set . Where did the First Set come from ? God , Or.........?



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