For Pythagorus in ancient Greece, mathematics was a religion. Why does the square of the two sides of a right angle triangle equal the square of the hypotenuse? No reason that I have ever been able to find. That’s the magic of the religion. Why does E=m times c squared? With math you can find this magic, but you can’t explain why or even how the magic works.
There’s quite a famous example of the ubiquitous nature of maths (in this case, arithmetic) that goes like this:
Prove that 2+1=3.
I’ll leave that to you :)
One thing that always bugs me about any knowledge is that it is all made up by humans to try and explain things. Maths isn’t the truth, it’s just a concept that has been developed over time, by many people, to try and help us along.
E=mc2 only because Einstein says it does. For instance, if someone else defines the parameters differently, then Q=FG/6x, if you want it to. Not quite as catchy, though.
I recall that geometry has some lemmas that you have to start with, that you just have to take ‘on faith’ as it were. Always bothered me.
That’s why a DI-lemma is so bothersome; you’re trying to believe two contradictory things at the same time! Mind-bending!
But then there’s the marvel of the Golden Ratio, of 1.618… that the ancients thought was the perfect proportion for a painting. And a basis for Archimedes’ Spiral, the shape of the Chambered Nautilus, who moved into a larger space as he outgrew his old quarters.
It’s related directly to the Fibonnacci series of 1, 1, 2, 3, 5, 8, 13, (the next one is the sum of the last two). somewhere about thirty, the ratio of the two becomes – you guessed it!
And the wonderful Penrose tiles (thanks, Roger!), kites and darts from a five-pointed star, that you can ‘tile the plane’ with but it doesn’t repeat; just recently learned, the ratios of the sides of those is – yup!
(I want to make some for a patio; anybody know a mold?)
I’m just reading “The Math Gene. How Mathematical Thinking Evolved and Why Numbers Are Like Gossip” by Keith Devlin - an in a way he says the same as Calvin does!
My personal favorite is the “proof” that 1 = -1. It’s obviously a flawed proof; but I have yet to see anyone give a satisfying explanation as to why it’s flawed.
There’s more truth to Calvin’s theory than most people would care to admit.
On the other hand, since the extent of Calvin’s ‘math’ at this point isn’t anything beyond simple arithmetic it could just be that he’s being an awkward lazy little smartarse. Someone should give him an abacus if he needs constant evidence that 2+3=5.
I suspect that any such false equation as 1 = -1 involves dividing by zero, which is rightly forbidden. If memory serves Wikipedia devotes a page to the issue and there are undoubtedly other references on the Web and in hard copy that do.
Folks, like it or not all human thinking has to proceed from axioms (things that are accepted “on faith”) - otherwise we couldn’t think at all. There is no such thing as metaphysical neutrality and only overemphasis on some human cognitive processes at the expense of others keeps some people from seeing this.
Mathematical rules are for fools. Calvin, you are supposed to break rules. Rules are meant to be broken. Your reasoning has better sense than the sense in maths.
1 = sqrt(1) = sqrt((-1)(-1)) = sqrt(-1) sqrt(-1) =i x i = -1.
The fallacy is that the rule sqrt(xy) = sqrt(x) sqrt(y) is generally valid only if at least one of the two numbers x or y is positive, which is not the case here.
Yes; but then the question is why that rule isn’t valid if both numbers are negative. Most answers that I’ve received have been some version of “because otherwise this nonsensical proof would work.”
Johanan Rakkav א said it pretty well: there will always be something that’s taken on faith.
Take a theoretical math course. I won’t go into great detail, but you will learn that 2+2 does not equal 4. It is theoretically impossible to have 2 exactly equal objects so there is no real 2. Basically you can use math to disprove most (if not all) of the accepted “rules” and “truths” about math.
On the 1 = -1 “proof”:
Part of it appears chopped off for me bu I can guess how it goes. The problem is clearly in splitting sqrt(-1 * -1) into sqrt(-1) * sqrt(-1). I don’t know why.
But our math system is flawed in its foundations in that it was built based on our perception of the world. First integer numbers (counting finite things), then decimals, then negative numbers (which have no physical meaning), then imaginary numbers (which only go to show that our math system is lacking). Or think about numbers like pi, e, sqrt(2), 10/3 etc which have an infinite number of decimal digits (so their exact value cannot be represented), yet geometry allows you to definitely divide a 10cm piece of paper in 3 exactly equal parts which is a contradiction. Or think of all the ugly constants in physics, that have seemingly arbitrary values.
My theory is that the world is too well structured (in all scales, from galaxies to quarks) to be ruled by such ugly values. There must be a physics/math system, where all these ugly numbers are actually simple and sensible and where calculation don’t come with conditions attached.
Come on, folks. Math is not some made up system; mathematicians are exploring a “found”, and you’d be surprised to find how interesting, system. People don’t make up theories, or even axioms, and then base their extensive studies on those. Axioms, such as 1+1=2, or two lines in a plane must cross if they are not parallel, are descriptions, not assumptions. The thing that’s hard to get is that math is derived from these axioms; everything, from the start, is “discovered”, not created.
Nor is math based on science, or vice-versa. Math is used as a tool in much scientific work, generally because it presents an elegant and pretty much universally accepted means of describing complex ideas, and which can be used to refute an idea as well as prove it. Conversely, there is much in math that has absolutely no application in science, or any other area of study except itself.
Arithmetic, geometry, trig, etc., are all basic tools of math; if they are not mastered then it is likely there will be no understanding of advanced math, or its concepts.
That is what is missed in this whole discussion. Calvin is, I think, being purposely obtuse, but merely to make a point, and that point is less obvious than it seems …
As a non-screaming ‘pinhead’ (a liberal atheist firmly in favor of separation of church and state), I feel awe and wonder at the marvels of the universe when I read scientific publications and learn about new developments in science.
That you somehow take those same marvels as an argument for imposing religious rituals and beliefs on our diverse society (and that you have to throw name-calling into the mix) only exposes your own narrowness of mind and thought.
Pinhead, indeed!
Dberrymanal1 said, about 6 hours ago
Good point! Let the pinheads who are always screaming about seperation of church and state put THAT in their pipes and smoke it.
Well, today’s strip certainly should be brought up to the anti-evolutionists - it is the final proof they need to show that science is just another religion. ;-)
You make a major error by calling maths a dead language with rigid rules - in fact ( I have this from my uncle, who taught post doctoral mathematics for forty years at Lehigh) maths is constantly evolving, changing, exploring, the grammar is flexible and under constant growth.
Maybe you need to go back and re-examine some other assumptions you make given this misunderstanding about maths.
Come on! You people are making my mind hurt. Just treat Math like music. It exists in it’s own self and we can use it in a lot of ways. And without math, we would have no meter or intervals in music. Mr Waterson is no man in a cave on a mountain: I bet he forgets his phone number or social security numer too.
@JAMEJO: “Axioms, such as 1+1=2, or two lines in a plane must cross if they are not parallel, are descriptions, not assumptions.”
Are you familiar with Non-Euclidean Geometry? You’re technically correct in what you state above, since the geometric definition of “parallel lines” is that they don’t cross and that they’re in the same plane. But that’s not one of the geometric axioms; the geometric axiom involving parallel lines states how many parallels there are to a given line that pass through a given point. Euclidean Geometry assumes that there is exactly one; but there are other geometries that make different assumptions (e.g., none, or an infinite count of them).
And then there’s Godel’s incompleteness theorem, which essentially states that any consistent mathematical system will necessarily include facts that cannot be proven, and must be taken “on faith”, as it were.
AFAICT, nobody here is saying that math is arbitrary, and can be anything we want it to be if we only believe hard enough, or any such rubbish. But neither is it devoid of assumptions. Math is a wonderful tool, with infinite possibilities; but even infinite potential has its limits.
@elbeck: “And just what the heck does the square root of negative one (the imaginary number) look like?”
Just take a step to your left…
@Fer Lefer: “My favorite “Heresy””
That’s a trivial one: you forgot to change the > to a < when you reversed the signs in the second-to-last step.
FYI, there is a simple and elegant proof of pythagorus’s theorum that doesn’t need more knowledge than that the area of a square is x^2: http://math4allages.files.wordpress.com/2010/02/pythagrean41.png
The best decision I made in High School was dropping Geometry and taking typing. Typing has served me well in my career and since I have been commenting here at gocomics my speed has increased tremendously. Proving, reading the comics can develop skills. So bring on the funnies!
My first-ever comment after lurking for several weeks. pbarnrob and dataweaver: you two have caused me to open up Wikipedia in another tab. Thanks so much for sharing! I’ve always been fascinated by math, and you’ve provided impetus to resume studies…I’m 59. Thanks again!
Say what you will, but for seeking “absolute truth,” I’ll trust that system that is consistent regardless of language, cultural backdrop, and literary styles over a bundle of myths, each as valid as another yet fully contraditory to one another…
There are three major “monotheistic” religions in the world, and countless other polytheistic faiths and an assortment of other “spiritual” movements and beliefs in the world, yet the “monotheistic” faiths cannot even agree on how the world started, let alone the nature of (G)od. Shoot, Christians can’t even agree on what Jesus’s message really means, or even WHAT Jesus was in the first place…
On the other hand, 1 + 1 = 2, regardless of whether you’re in India, Germany, Canada, or Mozambique, and so far, nobody has ever waged a “crusade” or “jihad,” or issued a “fatwah” or a “bull” over how to interpret the Liebnitz, Newton, or Pythagoras.
Plagiarized from a forgotten teacher from MANY years ago: “Why do you particularly dislike proofs? A proof is just a problem for which you know the answer.”
Whitehead and Russell’s Principia Mathematica is famous for taking a thousand pages to prove that 1+1=2. Of course, it proves a lot of other stuff, too. If they had wanted to prove only that 1+1=2, it would probably have taken only half as much space.
And, were they to use modern notation and other ways to save space and repetition, they could cut that even further, to maybe 200 pages.
Still, it takes a lot of work to start from just elementary principles to get to anything very substantial.
dataweaver said, about 7 proofs ago
Yes; but then the question is why that rule isn’t valid if both numbers are negative. Most answers that I’ve received have been some version of “because otherwise this nonsensical proof would work.”
Actually, it works from the rules of logic. As long as there is only one possible result, which means defining square roots as the positive one, and not removing “factors” of zero, any logical results will follow. However, once you introduce more than one possible result, you have to show that each combination leads to the proper result.
I’ve always felt the math is not a science, but rather akin to philosophy. You set up a world along with rules. And as long as one follows the rules, everything else follows logically.
Oh, and it does help if the world mirrors reality. But that’s not really a necessity.
Comics are more fun to read than math.
Wasnt there a great math teacher in history that confused the rulers of the day,was sentenced to death.?
By voluntarily drinking hemlock .
There is none but the one. Raised to any power, is still one. Anything raised by the power of one is unchanged, but anything raise by the power of nothing is one. One is equal to minus one, just not in the same direction, but it’s still one. The only part you have to take on faith is when we tell you what one is. Which one? The one that works. The one that doesn’t is invalid, but we can describe that one, too. Sometimes one that seems just fun or imaginary turns out to be useful. Keep on plaing those mind games forever. It’s lonely, but it’s the one.
It’s funny, I have a Bachelor’s degree in Math for the same reason I have a Master’s degree in Bible; because I like how things are either right or wrong, and opinions don’t enter into it.
You can kick and scream and throw a tantrum about how 2+2 ought to be 5, or how much you think 2+2=5, but that doesn’t make it so. Same thing, it doesn’t matter what you think the Bible ought to say; what does it say?
The Tiger’s observation to call a lawyer is wonderfully wry, since he IS one, and Calvin is simply one in training. Like Calvin, I was always really good at mathematics until we got to addition and subtraction…..
My comment to HOBBES yesterday was believing in what I could not prove was “Faith.” And today the story uses that theme. The math talk was way over my head, but I thought the strip was very cute. Wonder what HOBBES (commenter) is planning on for after Easter, as he said he was moving on to another something. Sigh. Hope he doesn’t forget us.
Complex math equations always did make my head hurt when I was in school (I guess you’ve either got the smarts for it or you don’t — and I certainly didn’t!) and now, all this math-speak here today is probably going to take me back kicking and screaming to my high school days and give me nightmares regarding those bad old days in my sleep tonight!!!!!
As a mathematician and a daily reader of this forum, I am pleased to see the wide array of participation today.
Why does mathematics generate such passion one way or the other? My colleague Reuben Hersh addresses this query in his recently published
LOVING + HATING MATHEMATICS.
I wonder what Hobbes would have said had he not left our forum for vacation.
Responding to a few things I’ve been reading up above:
Very well said, Wildcard24365! Excellent description of the difference between the science of math and the myths of religion.
As for algebra, Calvin did have an algebra problem on a test once (advanced for his age, yes, but this is a comic strip after all) and Tracer Bullet came to the rescue - with predictable results!
Such Wonder !!! the Beautiful simplicity of Facts and Figures,…, Mathematics
Its not a languge, or a religion or a hidden form of oriental torture
Mathematics is more eloquently, the musical score that describes the Symphony of the Universe
There is no real difference in the collective counting of grains of sand on a beach from the market inventory in a warehouse
Merchants have used fingers and toes to understand the commercial market while
Mathematicians and historians watch the stars to see beyond their own experience, well before their time or experience, ….,or dare to peer diligently into the magnifying glass at the intricate wonders of the truly small.
But What is math….???
Simply the full part score of God’s Creation that does not defy, yet describes in multiple levels of tolerance based upon the level of technical description….
Simple mathematics are no more than a counting scheme or definition of simple geometries as they regard to observed and reproducible physical occurrences, each set in real parts of Science form Physics to Biology, or Ecology or Geology or Medicine or ,……..
Harmonies and discords can be found in the correlations of frequency and time (neither of which is linear)
but what is math..????
no more than the symbolic representation of the real universe, to be simultaneously accepted and taken for granted,….., and as a tool of varying sharpness that is used by the casual observer to describe their own position with regard to their own personal understanding of the universe….
Calvin may well learn from his namesake “Lord Calvin” that “the description and exploration of the known world begins with the understanding of the unknown” ….
This challenge of understanding is education, another circular process that painfully starts and never ends
Do your homework and ask questions that they cannot answer
Wow! I go away on vacation and return to this!!!
Personally I just like the beauty and symmetry. But remember what Bertrand Russel said “Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. ” and let’s not forget Albert Einstein ,who by the way has a birthday on Monday , who said “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. ” This seems like good advice to you Calvin!
quite right little fellow, I always felt that too… having to simply believe that 2 and 3 is five and so on…
there is no proof for it, it is just accepted rules
and agreements among scientists
Leave Calvin alone, he’s right to be a (m)atheist.
As I told my students in evolution courses, I don’t care what you BELIEVE the course is evolution and I’ve got the pen in my hand – so learn it or else – and nobody is making you take this course.
As someone who struggled with math/arithmetic and wished that it was as easy as English, Lit,History and Science….I say Hurray for this delightful C&H I found it quite satisfying, Mr. Watterson, and I won’t attempt to analyse it!
I struggled with math all the way through high school until i took trignometry and then it just all kind of clicked and i got an a+ on that course. howsoever, i wish people would not over-analyze comics. someone commented that comics would not make your brain rot, but if a simple comic about math can stir up that much of a ruckus, then i might have to rethink reading comics…. QUIT RUINING THE COMICS YOU IDIOTS!!!
chamin about 13 years ago
Math atheist -> Matheist Long live atheists and matheists~!
LittleSister18 about 13 years ago
Wait! So all this time we were forced to learn math against our will.
rentier about 13 years ago
Atheist - Matheist - Theist - Deist.
GROG Premium Member about 13 years ago
I don’t think so, Calvin. Unlike Religion, the answers to math questions can be proven.
Good morning. Marg, Mike & ♠Lonewolf♠!
chovil about 13 years ago
For Pythagorus in ancient Greece, mathematics was a religion. Why does the square of the two sides of a right angle triangle equal the square of the hypotenuse? No reason that I have ever been able to find. That’s the magic of the religion. Why does E=m times c squared? With math you can find this magic, but you can’t explain why or even how the magic works.
Yukoner about 13 years ago
Calvin, don’t you want to be a mathemagician?
titanicus about 13 years ago
@Grog:
There’s quite a famous example of the ubiquitous nature of maths (in this case, arithmetic) that goes like this:
Prove that 2+1=3.
I’ll leave that to you :)
One thing that always bugs me about any knowledge is that it is all made up by humans to try and explain things. Maths isn’t the truth, it’s just a concept that has been developed over time, by many people, to try and help us along.
E=mc2 only because Einstein says it does. For instance, if someone else defines the parameters differently, then Q=FG/6x, if you want it to. Not quite as catchy, though.
pbarnrob about 13 years ago
I recall that geometry has some lemmas that you have to start with, that you just have to take ‘on faith’ as it were. Always bothered me.
That’s why a DI-lemma is so bothersome; you’re trying to believe two contradictory things at the same time! Mind-bending!
But then there’s the marvel of the Golden Ratio, of 1.618… that the ancients thought was the perfect proportion for a painting. And a basis for Archimedes’ Spiral, the shape of the Chambered Nautilus, who moved into a larger space as he outgrew his old quarters.
It’s related directly to the Fibonnacci series of 1, 1, 2, 3, 5, 8, 13, (the next one is the sum of the last two). somewhere about thirty, the ratio of the two becomes – you guessed it!
And the wonderful Penrose tiles (thanks, Roger!), kites and darts from a five-pointed star, that you can ‘tile the plane’ with but it doesn’t repeat; just recently learned, the ratios of the sides of those is – yup!
(I want to make some for a patio; anybody know a mold?)
Lots of magic in our Universe; ain’t it Grand?
Dberrymanal1 about 13 years ago
Good point! Let the pinheads who are always screaming about seperation of church and state put THAT in their pipes and smoke it.
Tineli about 13 years ago
I’m just reading “The Math Gene. How Mathematical Thinking Evolved and Why Numbers Are Like Gossip” by Keith Devlin - an in a way he says the same as Calvin does!
zeeny about 13 years ago
And I thought I was the only one being forced to learn maths :(
dataweaver about 13 years ago
My personal favorite is the “proof” that 1 = -1. It’s obviously a flawed proof; but I have yet to see anyone give a satisfying explanation as to why it’s flawed.
There’s more truth to Calvin’s theory than most people would care to admit.
GrimmaTheNome about 13 years ago
On the other hand, since the extent of Calvin’s ‘math’ at this point isn’t anything beyond simple arithmetic it could just be that he’s being an awkward lazy little smartarse. Someone should give him an abacus if he needs constant evidence that 2+3=5.
Rakkav about 13 years ago
I suspect that any such false equation as 1 = -1 involves dividing by zero, which is rightly forbidden. If memory serves Wikipedia devotes a page to the issue and there are undoubtedly other references on the Web and in hard copy that do.
Folks, like it or not all human thinking has to proceed from axioms (things that are accepted “on faith”) - otherwise we couldn’t think at all. There is no such thing as metaphysical neutrality and only overemphasis on some human cognitive processes at the expense of others keeps some people from seeing this.
hagarthehorrible about 13 years ago
Mathematical rules are for fools. Calvin, you are supposed to break rules. Rules are meant to be broken. Your reasoning has better sense than the sense in maths.
GrimmaTheNome about 13 years ago
Here’s the 1=-1 ‘proof’
1 = sqrt(1) = sqrt((-1)(-1)) = sqrt(-1) sqrt(-1) =i x i = -1.The fallacy is that the rule sqrt(xy) = sqrt(x) sqrt(y) is generally valid only if at least one of the two numbers x or y is positive, which is not the case here.
Frogman_tg about 13 years ago
I wonder what would have happened if I told my teacher that! then follows “But why do you want to see my parents?”
dataweaver about 13 years ago
Yes; but then the question is why that rule isn’t valid if both numbers are negative. Most answers that I’ve received have been some version of “because otherwise this nonsensical proof would work.”
Johanan Rakkav א said it pretty well: there will always be something that’s taken on faith.
djalmaferreira about 13 years ago
Calvin is a genius!!!!!!
mike.firesmith about 13 years ago
**Good morning Marg! Good morning Fran! Good Morning L’Wolf! Good Morning Grog!**
The lad is on to something. Even the bible says, “Go forth and multiply!”
tbree about 13 years ago
Wasn’t it Noah that got adders (snakes) to multiply by using a log table? (Which he made)
marvelljones about 13 years ago
Take a theoretical math course. I won’t go into great detail, but you will learn that 2+2 does not equal 4. It is theoretically impossible to have 2 exactly equal objects so there is no real 2. Basically you can use math to disprove most (if not all) of the accepted “rules” and “truths” about math.
Elaine Rosco Premium Member about 13 years ago
Calvin…you are just to clever…lol
UsernameInUse about 13 years ago
On the 1 = -1 “proof”: Part of it appears chopped off for me bu I can guess how it goes. The problem is clearly in splitting sqrt(-1 * -1) into sqrt(-1) * sqrt(-1). I don’t know why.
But our math system is flawed in its foundations in that it was built based on our perception of the world. First integer numbers (counting finite things), then decimals, then negative numbers (which have no physical meaning), then imaginary numbers (which only go to show that our math system is lacking). Or think about numbers like pi, e, sqrt(2), 10/3 etc which have an infinite number of decimal digits (so their exact value cannot be represented), yet geometry allows you to definitely divide a 10cm piece of paper in 3 exactly equal parts which is a contradiction. Or think of all the ugly constants in physics, that have seemingly arbitrary values.
My theory is that the world is too well structured (in all scales, from galaxies to quarks) to be ruled by such ugly values. There must be a physics/math system, where all these ugly numbers are actually simple and sensible and where calculation don’t come with conditions attached.
witewater about 13 years ago
Watterson seems to be commenting on the current skepticism of the sciences that festering in our society…
@chovil here is the explaination that I was given to your question :<>
http://www.homeschoolmath.net/teaching/pythagorean-theorem-elementary.php
It gives you a graphic example of how Pythagoras was inspired to develop the formula. it is VERY concrete. no faith necessary
Packratjohn Premium Member about 13 years ago
Meet the new Math, same as the old Math….
mac47 about 13 years ago
So much for church and state in public schools.
calvinandquestionmark about 13 years ago
Matheists favorite part of the Bible is in the Old Testament…Numbers.
jonathan.james about 13 years ago
Come on, folks. Math is not some made up system; mathematicians are exploring a “found”, and you’d be surprised to find how interesting, system. People don’t make up theories, or even axioms, and then base their extensive studies on those. Axioms, such as 1+1=2, or two lines in a plane must cross if they are not parallel, are descriptions, not assumptions. The thing that’s hard to get is that math is derived from these axioms; everything, from the start, is “discovered”, not created.
Nor is math based on science, or vice-versa. Math is used as a tool in much scientific work, generally because it presents an elegant and pretty much universally accepted means of describing complex ideas, and which can be used to refute an idea as well as prove it. Conversely, there is much in math that has absolutely no application in science, or any other area of study except itself.
Arithmetic, geometry, trig, etc., are all basic tools of math; if they are not mastered then it is likely there will be no understanding of advanced math, or its concepts.
That is what is missed in this whole discussion. Calvin is, I think, being purposely obtuse, but merely to make a point, and that point is less obvious than it seems …
paullp Premium Member about 13 years ago
Dberrymanal1,
As a non-screaming ‘pinhead’ (a liberal atheist firmly in favor of separation of church and state), I feel awe and wonder at the marvels of the universe when I read scientific publications and learn about new developments in science.
That you somehow take those same marvels as an argument for imposing religious rituals and beliefs on our diverse society (and that you have to throw name-calling into the mix) only exposes your own narrowness of mind and thought.
Pinhead, indeed!
Dberrymanal1 said, about 6 hours ago
Good point! Let the pinheads who are always screaming about seperation of church and state put THAT in their pipes and smoke it.
rentier about 13 years ago
Chovil So it is, in the end it is an akt of belief it!
wilorg about 13 years ago
Well, today’s strip certainly should be brought up to the anti-evolutionists - it is the final proof they need to show that science is just another religion. ;-)
wilorg about 13 years ago
Nab,
You make a major error by calling maths a dead language with rigid rules - in fact ( I have this from my uncle, who taught post doctoral mathematics for forty years at Lehigh) maths is constantly evolving, changing, exploring, the grammar is flexible and under constant growth.
Maybe you need to go back and re-examine some other assumptions you make given this misunderstanding about maths.
dimeadance about 13 years ago
Come on! You people are making my mind hurt. Just treat Math like music. It exists in it’s own self and we can use it in a lot of ways. And without math, we would have no meter or intervals in music. Mr Waterson is no man in a cave on a mountain: I bet he forgets his phone number or social security numer too.
wilorg about 13 years ago
Seems to me there are lots of Math Atheists currently in the state legislatures and in Congress.
dataweaver about 13 years ago
@JAMEJO: “Axioms, such as 1+1=2, or two lines in a plane must cross if they are not parallel, are descriptions, not assumptions.”
Are you familiar with Non-Euclidean Geometry? You’re technically correct in what you state above, since the geometric definition of “parallel lines” is that they don’t cross and that they’re in the same plane. But that’s not one of the geometric axioms; the geometric axiom involving parallel lines states how many parallels there are to a given line that pass through a given point. Euclidean Geometry assumes that there is exactly one; but there are other geometries that make different assumptions (e.g., none, or an infinite count of them).
And then there’s Godel’s incompleteness theorem, which essentially states that any consistent mathematical system will necessarily include facts that cannot be proven, and must be taken “on faith”, as it were.
AFAICT, nobody here is saying that math is arbitrary, and can be anything we want it to be if we only believe hard enough, or any such rubbish. But neither is it devoid of assumptions. Math is a wonderful tool, with infinite possibilities; but even infinite potential has its limits.
@elbeck: “And just what the heck does the square root of negative one (the imaginary number) look like?”
Just take a step to your left…
@Fer Lefer: “My favorite “Heresy””
That’s a trivial one: you forgot to change the > to a < when you reversed the signs in the second-to-last step.
TheDOCTOR about 13 years ago
TheDOCTOR about 13 years ago
laevisx about 13 years ago
FYI, there is a simple and elegant proof of pythagorus’s theorum that doesn’t need more knowledge than that the area of a square is x^2: http://math4allages.files.wordpress.com/2010/02/pythagrean41.png
cleokaya about 13 years ago
The best decision I made in High School was dropping Geometry and taking typing. Typing has served me well in my career and since I have been commenting here at gocomics my speed has increased tremendously. Proving, reading the comics can develop skills. So bring on the funnies!
joelwmd about 13 years ago
And I thought the strip was just about Calvin trying to get out of doing homework?!
Kellie Johnson about 13 years ago
Amen, Calvin! Amen.
Stagefright1970 about 13 years ago
My first-ever comment after lurking for several weeks. pbarnrob and dataweaver: you two have caused me to open up Wikipedia in another tab. Thanks so much for sharing! I’ve always been fascinated by math, and you’ve provided impetus to resume studies…I’m 59. Thanks again!
mil4reloaded about 13 years ago
What is this a math forum!? Too much… My head is hurting now. LOL
Wildcard24365 about 13 years ago
Say what you will, but for seeking “absolute truth,” I’ll trust that system that is consistent regardless of language, cultural backdrop, and literary styles over a bundle of myths, each as valid as another yet fully contraditory to one another…
There are three major “monotheistic” religions in the world, and countless other polytheistic faiths and an assortment of other “spiritual” movements and beliefs in the world, yet the “monotheistic” faiths cannot even agree on how the world started, let alone the nature of (G)od. Shoot, Christians can’t even agree on what Jesus’s message really means, or even WHAT Jesus was in the first place…
On the other hand, 1 + 1 = 2, regardless of whether you’re in India, Germany, Canada, or Mozambique, and so far, nobody has ever waged a “crusade” or “jihad,” or issued a “fatwah” or a “bull” over how to interpret the Liebnitz, Newton, or Pythagoras.
I kinda find that attractive.
anobium625 about 13 years ago
Plagiarized from a forgotten teacher from MANY years ago: “Why do you particularly dislike proofs? A proof is just a problem for which you know the answer.”
bmonk about 13 years ago
Whitehead and Russell’s Principia Mathematica is famous for taking a thousand pages to prove that 1+1=2. Of course, it proves a lot of other stuff, too. If they had wanted to prove only that 1+1=2, it would probably have taken only half as much space.
And, were they to use modern notation and other ways to save space and repetition, they could cut that even further, to maybe 200 pages.
Still, it takes a lot of work to start from just elementary principles to get to anything very substantial.
dataweaver said, about 7 proofs ago
Yes; but then the question is why that rule isn’t valid if both numbers are negative. Most answers that I’ve received have been some version of “because otherwise this nonsensical proof would work.”
Actually, it works from the rules of logic. As long as there is only one possible result, which means defining square roots as the positive one, and not removing “factors” of zero, any logical results will follow. However, once you introduce more than one possible result, you have to show that each combination leads to the proper result.
Or, in logical (Polish) notation: Aw1w2, (w1 –> w3), (w2 –>w3) —> w3.
All I can say is wait until Calvin gets to Algebra or Diophantine equations.
SWEETBILL about 13 years ago
YEA, wait Calvin till Obama does his math on your paycheck before you get it
rshive about 13 years ago
I’ve always felt the math is not a science, but rather akin to philosophy. You set up a world along with rules. And as long as one follows the rules, everything else follows logically.
Oh, and it does help if the world mirrors reality. But that’s not really a necessity.
ratlum about 13 years ago
Comics are more fun to read than math. Wasnt there a great math teacher in history that confused the rulers of the day,was sentenced to death.? By voluntarily drinking hemlock .
ChukLitl Premium Member about 13 years ago
There is none but the one. Raised to any power, is still one. Anything raised by the power of one is unchanged, but anything raise by the power of nothing is one. One is equal to minus one, just not in the same direction, but it’s still one. The only part you have to take on faith is when we tell you what one is. Which one? The one that works. The one that doesn’t is invalid, but we can describe that one, too. Sometimes one that seems just fun or imaginary turns out to be useful. Keep on plaing those mind games forever. It’s lonely, but it’s the one.
alan.gurka about 13 years ago
OMG! Am I going to burn in hell, now that I have embraced math?
Captain_Commando about 13 years ago
Grog said, “I don’t think so, Calvin. Unlike Religion, the answers to math questions can be proven.”
This from a guy who has a Johnny Hart character as his avatar
ReliantOne about 13 years ago
I don’t know how you did it, but somehow you managed to suck the fun right out of today’s strip.
soundpreacher about 13 years ago
It’s funny, I have a Bachelor’s degree in Math for the same reason I have a Master’s degree in Bible; because I like how things are either right or wrong, and opinions don’t enter into it.
You can kick and scream and throw a tantrum about how 2+2 ought to be 5, or how much you think 2+2=5, but that doesn’t make it so. Same thing, it doesn’t matter what you think the Bible ought to say; what does it say?
tqnism about 13 years ago
That is my favorite Calvin strip.
batmanwithprep about 13 years ago
Preach!
Bluewolfmike about 13 years ago
15 mL of water + 15 mL of alcohol = 28 mL
1 female dog + 1 male dog = 3-10 dogs
George Arnold about 13 years ago
And Calvin is just having trouble with simple math.
dvoyack about 13 years ago
Numbers and letters together??? Blasphemy!!!! Down with Algebra!!! it’s the devil’s plaything!!!
LeStats about 13 years ago
Wait until he has to learn The Calculus!
khpage about 13 years ago
The Tiger’s observation to call a lawyer is wonderfully wry, since he IS one, and Calvin is simply one in training. Like Calvin, I was always really good at mathematics until we got to addition and subtraction…..
gofinsc about 13 years ago
bleeep, it’s too bad Hobbes isn’t here to fill up a full page with commentary and philosophy on this subject.
Mythreesons about 13 years ago
My comment to HOBBES yesterday was believing in what I could not prove was “Faith.” And today the story uses that theme. The math talk was way over my head, but I thought the strip was very cute. Wonder what HOBBES (commenter) is planning on for after Easter, as he said he was moving on to another something. Sigh. Hope he doesn’t forget us.
Gretchen's Mom about 13 years ago
Complex math equations always did make my head hurt when I was in school (I guess you’ve either got the smarts for it or you don’t — and I certainly didn’t!) and now, all this math-speak here today is probably going to take me back kicking and screaming to my high school days and give me nightmares regarding those bad old days in my sleep tonight!!!!!
apGwilym about 13 years ago
one’s not half two. It’s two are halves of one:
Take it as an axiom. The rest of the poem is more complicated than Boolian algebra.
kevin87031 about 13 years ago
As a mathematician and a daily reader of this forum, I am pleased to see the wide array of participation today.
Why does mathematics generate such passion one way or the other? My colleague Reuben Hersh addresses this query in his recently published LOVING + HATING MATHEMATICS.
I wonder what Hobbes would have said had he not left our forum for vacation.
glitterygal07 about 13 years ago
I’m guessing Calvin’s religion is math?
paullp Premium Member about 13 years ago
Responding to a few things I’ve been reading up above:
Very well said, Wildcard24365! Excellent description of the difference between the science of math and the myths of religion.
As for algebra, Calvin did have an algebra problem on a test once (advanced for his age, yes, but this is a comic strip after all) and Tracer Bullet came to the rescue - with predictable results!
DrCarlson about 13 years ago
Such Wonder !!! the Beautiful simplicity of Facts and Figures,…, Mathematics Its not a languge, or a religion or a hidden form of oriental torture Mathematics is more eloquently, the musical score that describes the Symphony of the Universe There is no real difference in the collective counting of grains of sand on a beach from the market inventory in a warehouse Merchants have used fingers and toes to understand the commercial market while Mathematicians and historians watch the stars to see beyond their own experience, well before their time or experience, ….,or dare to peer diligently into the magnifying glass at the intricate wonders of the truly small. But What is math….??? Simply the full part score of God’s Creation that does not defy, yet describes in multiple levels of tolerance based upon the level of technical description…. Simple mathematics are no more than a counting scheme or definition of simple geometries as they regard to observed and reproducible physical occurrences, each set in real parts of Science form Physics to Biology, or Ecology or Geology or Medicine or ,…….. Harmonies and discords can be found in the correlations of frequency and time (neither of which is linear) but what is math..???? no more than the symbolic representation of the real universe, to be simultaneously accepted and taken for granted,….., and as a tool of varying sharpness that is used by the casual observer to describe their own position with regard to their own personal understanding of the universe….
Calvin may well learn from his namesake “Lord Calvin” that “the description and exploration of the known world begins with the understanding of the unknown” ….
This challenge of understanding is education, another circular process that painfully starts and never ends Do your homework and ask questions that they cannot answer
DrCarlson
larney45 about 13 years ago
I’m an English teacher, fer heavens sake! All this math makes my brain hurt…
SWEETBILL about 13 years ago
@Linda Arney THANK YOU FOR MY LAUGH FOR TODAY. MY eyes hurt too :-)
kid1at3heart about 13 years ago
I was told for years that reading comics would ‘rot’ your brain! Obviously not true after reading all these math genius’ remarks.
JTGAM about 13 years ago
Wow! I go away on vacation and return to this!!! Personally I just like the beauty and symmetry. But remember what Bertrand Russel said “Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. ” and let’s not forget Albert Einstein ,who by the way has a birthday on Monday , who said “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. ” This seems like good advice to you Calvin!
HyveALiveO about 13 years ago
quite right little fellow, I always felt that too… having to simply believe that 2 and 3 is five and so on… there is no proof for it, it is just accepted rules and agreements among scientists
Leave Calvin alone, he’s right to be a (m)atheist.
COWBOY7 about 13 years ago
Only Calvin can come up with a concept such as this!
G’Evening, Mike, Marg & Grog!
lindz.coop Premium Member about 13 years ago
As I told my students in evolution courses, I don’t care what you BELIEVE the course is evolution and I’ve got the pen in my hand – so learn it or else – and nobody is making you take this course.
hopeandjoy2 about 13 years ago
As someone who struggled with math/arithmetic and wished that it was as easy as English, Lit,History and Science….I say Hurray for this delightful C&H I found it quite satisfying, Mr. Watterson, and I won’t attempt to analyse it!
amusia007 about 13 years ago
We don’t need faith, we have fact. Descartes figured that out long ago: “Cogito ergo sum.” “I think, therefore I am.”
But wait… what if God thinks, and is just imagining us, and imagining that we’re just thinking?… why, that means… “Oh, noooooo…”
vibjyor about 13 years ago
I think this strip scored the highest comments in a very long long time
kevin87031 about 13 years ago
Linda, You’ll never hear a math teacher say, “All this English makes my head hurt!”
jeffreydahn about 13 years ago
Nabuquduriuzhur: It’s the “Planck” Era, and 10 to the -43 seconds, you pompous buffoon.
mcunningham422 about 13 years ago
Leave it to geeks to spoil a good cartoon. By the way, I teach math.
hobbes n kay about 11 years ago
I struggled with math all the way through high school until i took trignometry and then it just all kind of clicked and i got an a+ on that course. howsoever, i wish people would not over-analyze comics. someone commented that comics would not make your brain rot, but if a simple comic about math can stir up that much of a ruckus, then i might have to rethink reading comics…. QUIT RUINING THE COMICS YOU IDIOTS!!!