Math ability and intelligence

Avidya:So, is math ability synonymous with intelligence/thinking ability, or do you agree with my assessment that math is just a specific skill in the wider scheme of intelligence? Do you think its more important for me to learn math or just get over it?

Just get over it. Everyone has their strengths and weaknesses.

I knew an engineer who could quickly execute quite a few mathematical operations in his head when other people were reaching for their calculators. But his language skills were abysmal. Asking him to compose an articulate post on a philosophy forum would've been a complete waste of time.

I also knew a nurse who couldn't do math in her head to save her life, but her facility for medical diagnosis was recognised as profound.

Intuition: a semi-conscious process of perception and pattern-matching which enables quick problem-solving, judgement and decision-making.

Cognition: The combined operation of faculties used to represent, compare, modify, synthesize, organise, store, retrieve, communicate, and apply, knowledge.

Cognition is a slower process than intuition.

For a while, back in the 1970s was it? people liked to brag about whether they were "linear thinkers" or "non-linear" thinkers. I think "non-linear" was supposed to be cooler than "linear". That would be like, logic vs. intuition; step-by-step thinking vs. the leap to a conclusion, science vs. art. In fact, we all use both kinds of thinking all the time.

Quoting Avidya

I have a hard time with numbers. I could blame it at school, but that would only be partially true, because almost every other pupil exceeded me at math. Being almost innumerate hurts my self confidence.

I also have had a hard time with mathematics. I am not quite "innumerate", but my arithmetic skills have a low ceiling. Mathematic skill would have come in handy, but since I didn't have it, I coped one way or another, which is what people do.

How big a problem innumeracy is depend on what you want to do for a living. High finance is probably not going to work and neither is nuclear physics or chemistry. It also depends on the actual level of skills you possess. If you can manage the 4 basic functions (+, -, x, and ÷) in everyday kinds of situations, innumeracy might not be that big a problem. Your cell phone has a calculator on it. If you can't manage +, -, x, and ÷ then you probably have already developed some coping skills, just like people do who are dyslexic. We all figure out ways to get around our deficiencies whatever they are.

Don't know jack-shit about algebra? Geometry? Statistics? Billions of people have been very successful in life without knowing much about algebra. Most of the world's people have been illiterate since writing was invented, and yet managed to do just fine.

I am glad you brought this topic to discussion because it is something I have struggled with personally as well. A couple of years ago, I would have not worried about the links between mathematical/logical ability and general intelligence, but now it is an issue that deeply intrigues me. As someone who is very interested in politics, philosophy, and current affairs, and likes to argue in the rigorous and structured way that an analytic philosopher would, it concerns me that if I lack skill in an ability such as logic, I will be incompetent in political and philosophical discussions. And well, I can tell you what I have learned:

1. Empirically speaking, research does suggest that there is a G factor, or a general intelligence. This means that an individual's level of abilitiy in domains such as literature, math, logic,writing, and so on, are typically correlated.So if you are good at math, you are probably also good at english and writing. This is not to say that abilities across all of those domains are going to be equal, they can and will vary. Neither does it mean that there are'nt people who score really high on one (e.g. math) and are notably deficient in another (e.g. english). It just means that generally speaking, abilities across these domains are correlated. For a controversial but I believe sound conversation on this, look up Charles Murray's and Sam Harris podcast on youtube.

2. There is good news,contrary to disciplines such as history, politics, and other soft areas of study, the process of learning math is different in its nature. Becoming good with mathematical reasoning requires constant exposure to making mistakes. After practicing enough times, you are able to do things with ease. Neuroscientific research has shown that there are specific kinds of neurons, I believe they are called decision making neurons (pardon me if this is not the exact scientific jargon, im no scientist) which release dopamine whenever you are right about something, and fail to release it when you are wrong. These dopamine releasing neurons become trained with enough experience to tell you subconsciously when you are right about something, and release dopamine if you make the right decision. Whenever you are wrong, they constantly rewire themselves in order to detect the pattern in any situation which will yield the right answer. So, whenever you fail a math problem, your brain doesnt like the lack of dopamine release, and thus rewires itself to be able to identifiy what the right answer is in the next circumstance. I apologize if this explanation seems a bit untidy. If you want to learn more about it I recommend the book, "How We Decide" by Jonah Lehrer.

3. I was always average on math, but begun practicing with online resources such as The Great Courses Plus, there are also other didactic materials such as the For Dummies series, or the Wiley Self- Teaching Guides. Although these may not seem appealing at first, I guarantee you they will do wonders. All you need is constant practice, if you are smart enough to be concerned about your intelligence, you certainly have the ability to master mathematics. Furthermore, once you get the hang of it, it is a truly beautiful experience to observe how everything fits in perfectly. Again, all you need is constant practice, if you ask the average engineer or economist, they will invariably let you know about the amount of hours they spent banging their head against the wall trying to solve problems. I would encourage you to learn math, it will make you much more adept at reasoning in other domains.
There is a wonderful book that talks about this, it is called "How to Not be Wrong;The Power of Mathematical Thinking" by Jordan Ellenberg. In it, he explains, in layman's terms, how viewing the world through the prism of mathematics can help you weed out implausible conclusions in affairs that seem on the surface non-mathematical (e.g. politics, history, philosophy, etc.)

Anyways, I hope this helps. And as someone above mentioned, you dont necessarily need math to be succesful, it will depend on your area of study, but I would encourage you to learn it if you are interested in problems that are political and social in their nature, it helps you a lot in learning to structure your arguments.

One of the reason why math seems for many so different, something equivalent of making crossword puzzles and something opposite to using intuitive (or the "linear" thinking compared to "non-linear" thinking that Bitter Crank brought up), is in the way how mathematics is taught to us.

Put into a nutshell, we are taught math by doing algorithms: if you have a certain math question, you answer it using a certain algorithm. You get the correct answer and Presto! You are good in math. And here with algorithm I mean it in the more general sense: a self-contained sequence of actions to be performed, usually a computation. Proofs of the equations are just given and not much if anything goes to thinking about the issue or the philosophical side of math.

Hence the focus is in the ability to compute, to calculate, or then you are asked to give a proof, which usually itself is an algorithm itself. And those that learn to use these algorithms are rewarded and those who aren't so quick are seen (or feel) "not so good in math"). For many the "alphabet soup"-of higher math is very difficult to understand.

We have to remember that a lot of math can be explained by geometry, hence one can grasp mathematics also visually.

Also, mathematics is seldom if ever taught as a historical process, how a mathematician came up in the first place with the result he did. What was his background knowledge? How was it seen by his peers? Was it actually accepted? For me this kind of perspective helps a lot to understand the process. I'm not saying here that math is a "social construct" like many other things are, but that for me this approach makes the math more understandable.

Me too i always find math very hard. :(

Reply to Avidya Math ability and intelligence

Avidya – I must say that you are very high on the scale of people with courage. A very admirable trait which I am sure has served you well.

Speaking of math, as others have noted, it can be learned. It is really just like music. How do you get to Carnegie Hall – practice? Music is fundamentally mathematical. Since it is a self-esteem issue for you – it is important. Start slow with basic arithmetic and work your way up. At some point you will say to yourself – “I am good enough at math”. And then the issue of self-esteem will be gone – in relation to math. If you don’t do anything about it – the issue will fester and probably get worse. However I have confidence in you because you have courage.

I think you will find that your issues of self-esteem will always be with you. Human beings in my view are insecure for many reasons. We all have issues of self-esteem – forever. Best regards and good luck.

Quoting Avidya

It seems to me there are two types of thinking that I call "System 1" and "System 2". System 1 is the intutive, creative and visual part of your mind -- the part that instantly understands words without having to analyze them, and the part that engages in metaphorical and visual thinking. I consider myself fairly skilled in this department, because I have an intuitive sense for language, writing and visualization. I find that philosophers are generally very skilled in this department, and uses brilliant metaphors to describe the nature of reality. It seems to me that philosophy entails mind activity beyond mathematics and symbols to get to the very fabric of existence.

I also recognize two types of thinking. I call them making crap up and learning. Some people just make crap up, because they are to lazy to go out and learn. For example some people are bad at math, because they don't try hard enough and make excuses.

Quoting Jeremiah

I also recognize two types of thinking. I call them making crap up and learning. Some people just make crap up, because they are to lazy to go out and learn. For example some people are bad at math, because they don't try hard enough and make excuses.

I would call your response - uncompassionate. Some day the shoe will be on the other foot and you may need some compassion.

I agree with the OP that certain brains are wired in a more systematic way that can process and analyze data with more calculation than other brains. Although I thought I was was a more system 1 sort of guy but since I have been taking algebra and calculus at university I am coming to see that most people can learn it if they apply themselves (i flunked maths at school). Nevertheless the correlation with math wiz's and people who are almost autistic about understanding the in's and outs of life, romance, friends and the fine things like philosophy is not out of place. I put engineers into that category too.

What I want to know is... was this a phenomena before the age of enlightenment genetically? Or did it spawn after romanticism when generations were influenced by the trade of their forefathers?

Quoting woodart

I would call your response - uncompassionate. Some day the shoe will be on the other foot and you may need some compassion.

I think you are being over dramatic.

The numbers in math are fiction, they are creation of human mind, ever noticed how identical they are, each consist of equal parts of another. Super abstract concept. The numbers are not made up like this: zero is all embracing, 1 is , o well, I can't change what it is, it is just any first count of anything, that particular, you see. why 2 should be 1 and 1? Why can't it be it's own size independent of 1? 1 elephant is of course different than 1 geese or 1 ant... 1 planet is different from another 1 planet. Then we try to create farther, we came up with odd and even numbers! They do not exist! Anything can be divided equally by any number, at least sufficiently equally, in a quantitative sense, it's up to our abilities to do so. If we start speaking of qualitative division, oh, we'd be so screwed. Qualitative is different, you see. It has to align with each individual desire or necessity or personal, subjective value. Someone decide three of us can eat each a portion of dog stake. I will remain hungry because I won't eat the dog or I won't eat human flesh, or I won't eat dairy. Why take two people and divide between them four apples? As if in real life people won't be able to share 5 apples if needed? We start with simplifying things to death, falsifying and wrongly naming simplification points of our mind, which actually are called then by us "numbers". What do they numb? They numb our desire to really understand Universe and accept it for what it is. The Universe is not number, it is math-less mass or entity, or phenomenon. Why there can not be true global market? For the qualitative reasons of what's offered and what people are ready to accept and make use of without harming or remaking who they were for the most of their history.

Quoting Victoria Nova

The numbers in math are fiction, they are creation of human mind, ever noticed how identical they are, each consist of equal parts of another. Super abstract concept. The numbers are not made up like this: zero is all embracing, 1 is , o well, I can't change what it is, it is just any first count of anything, that particular, you see. why 2 should be 1 and 1? Why can't it be it's own size independent of 1? 1 elephant is of course different than 1 geese or 1 ant... 1 planet is different from another 1 planet. Then we try to create farther, we came up with odd and even numbers! They do not exist! Anything can be divided equally by any number, at least sufficiently equally, in a quantitative sense, it's up to our abilities to do so. If we start speaking of qualitative division, oh, we'd be so screwed. Qualitative is different, you see. It has to align with each individual desire or necessity or personal, subjective value. Someone decide three of us can eat each a portion of dog stake. I will remain hungry because I won't eat the dog or I won't eat human flesh, or I won't eat dairy. Why take two people and divide between them four apples? As if in real life people won't be able to share 5 apples if needed? We start with simplifying things to death, falsifying and wrongly naming simplification points of our mind, which actually are called then by us "numbers". What do they numb? They numb our desire to really understand Universe and accept it for what it is. The Universe is not number, it is math-less mass or entity, or phenomenon. Why there can not be true global market? For the qualitative reasons of what's offered and what people are ready to accept and make use of without harming or remaking who they were for the most of their history.

Pass the bong. It's legal in my jurisdiction.

I've been a mathematician for almost sixty years and have known good mathematicians with poor language skills and others with high language skills, colleagues who could write brilliantly and others who did poorly expressing themselves. Some had artistic talents, like sculpturing and carving lovely and exotic figures, and others lacked such talents. Some were accomplished musicians and others couldn't carry a tune. Some who were musicians could only play what others had created, while some could compose as well.

There is certainly a talent for mathematics, as there is for music, and, more often than one might suspect, mathematicians can have both. I don't. :sad:

Years ago I knew a professor who was recognized for his contributions in calculus of variations, but, to the amusement of his students, consistently made mistakes at the blackboard doing elementary fractions. The ability to mentally compute - what idiot savants excel at - is not essential for producing interesting mathematics. What is essential, beyond a native talent in the subject, is a desire and ability to explore and discover, to use one's imagination to create.

I was a rock climber for over sixty years, and have had a number of climbing friends who were mathematicians. That may seem odd, but both activities are exploratory and creative. The Brits in the 1880s used the word "problem" to describe unclimbed but appealing sections of rock, like questions in a text that required "solutions". Mathematicians and climbers are problem solvers. :cool:

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