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Seamus McGrenery

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If the human brain is an advanced computer why are people so bad at math?

We seem to be able to do all sorts of complicated computations in our everyday lives.

For example most young children can predict the pat of a moving ball and move to catch it. The same children often seem to have difficulty with quite simple math problems.

Even educated adults have problems with any kind of complex math. For example I guess most of us would be unable to calculate the path of a moving ball in a short time, let alone calculate the path we would need to move to catch a a ball while it is in the air.

When it comes to understanding statistics it seems that even trained scientists sometime have trouble with them.

Topics: Human Brain math
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Closing Statement from Seamus McGrenery

While the computer analogy has some value in giving us an understanding of how our brains work it also has limits. It seems to be difficult to program humans for certain types of task, possibly because our brains work significantly differently to binary computation.

In much of what we see and here about our minds there seems to be a diminishing of the body and how much our brains serve our bodies. So much of our mental function is devoted to maintaining our bodies environmental stability, fluid and nutrition requirements as well as finding a mate and protecting our offspring. The things we are good at show us the importance of these functions, but because they are so 'basic' we tend to take them for granted.

Two interesting points in relation to the average persons math ability are highlighted in the debate.

Programming is the first.
If we accept that, at least in part, our brains work like a computer then we have to accept that, again at least in part, it is programmable. While there is a suggestion that, potentially, a human brain could operate as a supercomputer, in terms of math, we do not seem to have learned how. So the positive from this is that we may learn to unlock a great deal more of our mental potential.
More problematic is how, and by who, are we programmed. There seems to be some agreement that learning is somehow akin to programming. My own view is that we have active filters on the information we receive and that these filters present the highest barriers to any information that could be interpreted programmatic.
Even that does not seem to explain the difficult humans have in learning and practicing certain types of mathematical operations.

Second is type of computation
Implicit in some of this debate is the assumption that our brains do not work by binary arithmetic. Discovering the type of computation we use may give us a clearer understanding of our limitations, and maybe a way to unlock some of that extra potential.

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    Mar 22 2013: Analogies, such as those between brain and computer, are helpful. But an analogy between two things doesn't mean the two things are identical.

    A brain, while great at things like storing and processing information (like a computer), is different in other critical ways. Whereas a computer is (mostly) completely logical, straightforward, linear / binary, the human brain is not. It's fuzzy and biased and instinctual and ... human.

    Thus, the way a computer processes math is going to be very different from the way a human brain does.
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    Mar 24 2013: Both the human mind and computers require a sufficient level of 'programming' to be used effectively. The human mind has the potential to better than an advanced computer, it just needs to be trained to 'operate' a certain way first
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      Mar 25 2013: We can learn something from thinking about the human mind as a computer, though as the discussion has highlighted the analogy is far from perfect.

      The really interesting point here is about programming. How are human brains programmed, and what control does the person being programmed have over the process?
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        Mar 25 2013: Programming starts in the womb, according to some studies. Babies perceive sounds and intuit meanings at a very young age. Based on that information, they have already started being programmed.

        An older child may be programmed based on beliefs of parents, communities, religions, etc. Whatever a child experiences can be part of the programming. Often times, children have no control over the process of programming. As a child developes more connections in the brain, more thinking ability, their programming may expand.

        As thinking, feeling adults, who may develope more cognitive skills, we have choices regarding how we program the brain.

        Human behaviors have always interested me, so I explore and read all I can about this topic. The brain studies they are doing now are fascinating. The fact that I had a brain injury years ago, and insisted on veiwing and exploring all the tests, charts, x-rays, MRIs, etc. was fascinating as well:>)
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          Mar 25 2013: What makes us human is an endlessly fascinating subject. Our minds and the world we have built with them are what makes us different from other animals.

          If we accept there is value in the computer analogy then we must accept that there is some form of programming. This raises some questions.

          Clearly we learn things, but is learning the same as being programmed? How else are we programmed? What, if any, control do we have over being programmed?
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        Mar 25 2013: We humans are indeed fascinating:>)

        I agree with the computer analogy, and use it often when speaking about brain function. When I was unconscious, after an accident, emergency craniotomy, kept alive on life support systems, clinically unconscious, and clinically close to death, I was aware on several different levels.

        Although the "program" that allowed me to speak and connect on a human level was damaged and not functioning, other "programs" WERE open and functioning. That is why I use the computer analogy, and many scientists are using the computer analogy when speaking about the brain as well, so I believe it has value when trying to understand it.

        I believe learning and programming are similar. We learn from the information around us....correct? Our brain stores the information...correct? We can connect with different information in our brain at different times....correct? I believe we are learning and programming with every life experience, in each and every moment. I believe the "control" we have, as thinking, feeling, intelligent adults, is awareness, which is a choice. We can be more....or....less.....aware of what information we are assimilating and how we are using it in any given moment.

        Sounds like a computer to me!!! LOL:>)
  • Mar 23 2013: Computers know nothing about math. Human programmers have created routines to perform given sets of calculations. They make these routines as short, fast, and accurate as possible. The lack of knowledge on the computer's part is illustrated by "bugs" that crop up from time to time where the programmer failed to accurately code for all contingencies. Furthermore, these computer programs typically set limits on the precision of calculations. For example, I have only found one calculator program that can answer 9^(9^9), admittedly a large number.

    On the other hand, several methodologies have been developed to improve the math performance of the average elementary school student. We would do well to investigate and adopt those techniques.
  • Mar 22 2013: Computers, or perhaps to be more direct, our modern digital computers, are very good at numbers, and excellent at remembering numbers.

    People are not. However, we are very good at making inferences, and excellent at making logical assumptions.

    We are basically good at the things that computers "suck at", and vice versa. Which is perhaps why we created them in the first place - we created tools to enhance our abilities in the fields that we are weakest at.

    Another way to look at it: Why are hammers so good at driving in nails? Because we needed a tool, hard enough and heavy enough to do the job more efficiently that our mere human hand, being soft and "squishy". We built a tool to help do the things we are bad at.

    "Need" is the mother of invention?
    • Mar 23 2013: You said it bro necessity is the mother of invention.
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      Mar 24 2013: Looking at computers as tools which increase our ability to do things with our minds, in the same way as other tools increase our ability to do things with our bodies gives us a good insight into our use of computers.

      They are almost always devices that enable humans to have superpowers (in communication, calculation data storage, design etc..) rather than devices that have intelligence themselves.
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    Apr 4 2013: From the outside, a human and a computer can both answer 4 + 4. But inside the human there's a conscious mind that has learned the answer. Inside the computer, the bits are loaded into registers and compared with logic gates. One is alive, the other isn't. Whether they're both machines is up for debate, but computers are not at all like the human mind, and I dare say the mind isn't at all like a computer.
  • Mar 26 2013: They say "Computer is as smart as a person using it." Frankly speaking computer is dumb. When you think about it, it's just a big collection of metal parts. Computers need programs installed on it to be useful. Imagine a computer with no operating system. It is just going to be a black screen staring at you. Even super advanced computers need a program that works. If human brain is like a super advanced computer, for sure we need some kind of program installed on our brain that we can utilize to solve problems. I guess in this case this "program" is considered as education or process of learning. I can't think of someone being as smart as a computer when that person haven't accumulated or learned any knowledge. We talk, do math, and write because we learned from our experiences.
    As much as basic ability of human brain to reason and solve problems matter in one's smartness, level of knowledge that one obtain is probably more important. Just my point of view in this question...
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      Mar 27 2013: If I understand you correctly you are saying the human brain is like an advanced computer with some ifs:

      - A computer needs some form of Firmware / BIOS to get started and an operating system to do anything. Therefore if the brain is like a computer it needs to have some equivalent system.

      - Computers are 'dumb' or are unable to accomplish any task until they are programmed for that task.
      Similarly humans need to be programmed to accomplish many tasks, and education and learning 'program' us to be able to act.

      - Humans have an ability to accumulate learning directly from experience as well as from learning.

      The ability of a specific person in relation to a specific mental task will be determined by a combination of 'basic ability' which is a bit like processor power learning (programming). In most instances learning and experience will have more impact on the ability to do something than innate ability.

      So if I read you right your view is that the way we are programmed, gain knowledge through learning and experience, is more significant than most differences in basic ability between individuals.
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    Mar 23 2013: It's even more surprising that dogs can catch balls too. Perhaps, most people are bad at calculations simply because they don't need them.

    http://www.ted.com/talks/daniel_wolpert_the_real_reason_for_brains.html

    I won't say that brains are advanced computers. Advanced computers are a poor mimicry of the brain. A friend of mine said "computers are as smart as a lawn mower". With this analogy, your question is similar to a question, why humans cannot mow grass as fast as a lawn mower?

    When we catch a ball, we operate by sensory feedback by observing how the ball moves and reacting to the changes in its movement until the movement of the ball and the movement of our hand converges in the "catch" event. It's a simple feedback system that does not have any complicated math in it - no "knowledge" of the laws of movements whatsoever. We would be able to do that even if the balls flew up instead of down. When we solve the same problem on paper, the situation is very different. There is no feedback. Computers operate very differently. They crunch the numbers at huge speeds. That's not what our brains do.
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      Mar 24 2013: Must watch the talk, thanks Arkady.

      Maybe the computer is the best analogy we have for the way the brain works at the moment because we have a very limited understanding of how it works.

      I have come across the idea that we use simple sensory feedback to adjust our position to catch a ball. The thing is I have not come across a system or device that we use as an analogy for a simple feedback system used to perform a complex task.
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        Mar 24 2013: Dan Wolpert mentions the robotic arm designed to pour water into a glass. It's a 3-year PhD project. I think, the algorithms our brain uses are way more simple than computers and don't require complex math at all.
        • Mar 24 2013: Why do you think that? It sounds interesting. My first thought was that it was do to the higher level of complexity in our arms but I'm not so sure........ What are your thoughts?
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        Mar 24 2013: Why do I think that? What do you think? Does it feel like you are crunching numbers in your head when you catch a ball or riding a bicycle? What our brain does is making connections between neurons and firing them in patterns in response to stimuli. It seems to be a completely different algorithm of solving problems. This is why humans may see playing chess and playing checkers as a similar activity or apply skills gained while riding a bicycle to learning downhill skiing. Last time when I was changing in a gym, I thought, what would it take to write an algorithm for a robot to take pants out of the bag, turn them from being inside out, and put them on two legs while maintaining balance? I think we solve this problem using the same algorithm as catching a ball or riding a bicycle. The technology is just not there yet to imitate it. Digital logic circuits don't grow connections with each other or react to stimuli - they only switch between 0 and 1 which is a great achievement, but far from imitating our organic "computers".
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      Mar 24 2013: I agree Arkady that "Perhaps, most people are bad at calculations simply because they don't need them"...and... "When we solve the same problem on paper, the situation is very different. There is no feedback".

      That was certainly the case for me! Since I was a kid, I never really liked math very much and did not do well with math simply because I could not see any use for it in my life....other than the basics of course.....I could not imagine a use in my life for advanced math.

      When I owned and managed elderly state and federally subsidized housing, I had to learn to manage a several hundred thousand dollar budget, submit monthly, quarterly and annual financial reports and budget projections, etc.

      At that point in my life, I needed the calculations, the challenge was clearly presented, and needed to be on paper. If I didn't do the calculations and submit the paperwork, I would not get the subsidy. There was definitly feedback, the process made sense to me at that point, and I enjoyed it once I got into it:>)

      BTW...I believe this to be true of most things in the life adventure. Most people will pursue and embrace information when/if it feels needed.
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        Mar 25 2013: I think this applies to all adult learning. We are likely to learn if we are motivated by an immediate need to apply teh learning.
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          Mar 25 2013: I think it applies to most humans....children as well. I think it's been proven that everyone is likely to learn when we are motivated by an immediate need, or when/if we have the motivation created with curiosity:>)
    • Mar 24 2013: Your right. That's all computers really are. Highly sophisticated tools. The pinnacle of our ability to even develope tools but a tool nonetheless. The king of tools.......... Wait ........ that title could be misleading. Lol!
  • Mar 23 2013: Quoting Carl Sagan: "Something as simple as the concept of the number one has an elaborate logical underpinning". Computers definitely crunch numbers more quickly than most, but they don't compute the concept of their operations. Our minds are bogged down by the excessive background noise of understanding, clouding the simple approach to the end result.

    If we examine the minds of people like Daniel Tammet, their narrow band of focus allows them to avoid the fog and see the answers faster than a computer. If we had gargantuan fore brains that could manage the overload puked forth by the subconscious processes or a more fine tuned Singulate Gyrus to direct workflow, we might be faster.

    I've always wondered why my mind is very capable of doing trillions of on the fly calculations that vary by the second to tell my hand where to be to catch a ball thrown in an arc at 50mph through a cross wind of 6 knots, a gravitational field of 9.8m/s^2, and a drag coefficient of 0.3, but can take several minutes to solve the same problem on paper.
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      Mar 24 2013: So seeing the tasks we give to computers as simple and few in number gives an insight.

      The fuzziness of the concept of the number 1 may be something we have to deal with. But at the same time we need to regulate our breathing and heart-rate, be alert for sudden dangers, be it a lion on the plain or a robber in the building, make sure we have enough food, interact with other humans, maintain our positions in hierarchies.

      Cutting down on the things we have to do does seem to improve our abilities.
    • Mar 24 2013: Referring to the third paragraph, sometimes people are masterfull naturals at what they do and couldn't explain there own technique. It's like the body has an intelligence unto itself. When somebody who plays music gets in the zone there's absolutely no thought because it's detrimental to playing.
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        Mar 25 2013: Good point Nathan. It summarizes, I think, some of what Arkady is saying in terms of human skills.

        One reason human intelligence is unlike a computer is that in part it uses other parts of the human body to accumulate and apply 'information' to perform specific tasks. So maybe when a task like catching a ball needs to be repeated all the brain needs to do is send a 'close on contact' signall to the hand.
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    Apr 2 2013: Because computers are machines programmed to perform mathematics. People are conscious beings. They experience and build their understanding of the world through their experience. Computers simply move bytes around mechanically and let functions fall into place.

    When you send 4 + 4 into a computer, the computer doesn't think about the answer. Rather the functions pass the information the way they were designed to and process it. It can and will never tell you 9. It has no mind and it doesn't learn. At best it programs itself, and only if designed to.
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      Apr 2 2013: Well I guess you are saying that a human mind is not like a computer. Or is it that describing the human mind as a computer might explain some basic abilities of the mind it does not capture some important qualities.

      Of course we could program a computer so that sometimes it will give the answer 9 to the question 4 + 4. For example we could ask the computer to add 4 x math random above 0.9 to 4 x math random above 0.9 and round the answer to a whole number. The question is why would we?

      Or to put it another way what is the value to us of having a mind that can produce the answer 9 when asked 4 + 4?
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    Mar 28 2013: .
    .
    It is because we did not need such math 10,000 years ago.
    Thus, we do not have such math programs bio-evolved in our soul.
    ..
    .
    (For details, see the 1st article, point 2(5) at
    https://skydrive.live.com/?cid=D24D89AE8B1E2E0D&id=D24D89AE8B1E2E0D%21283&sc=documents)
    .
    .
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      Mar 28 2013: If a computer is a good analogy for the human brain, then the human brain should show some evidence of computer like qualities.

      When it comes to learning many people seem to be saying there is also an analogy between learning and being programmed, though with significant differences.

      We know that humans can learn (be programmed) to complete complex mathematical tasks, but they are seen as difficult and an ability with this type of task is praised and rewarded.

      In contrast even basic computers (excuse the pun) can be programmed to complete such tasks and the tasks have come to be seen as simple for computers.

      Why is the brain = computer analogy not holding up here and what does it tell us?
  • Mar 24 2013: Random "wiring" configurations aside, the brain is not a mathematical engine.
    It has evolved as a Bayesian comparison engine that makes predictions as to what will happen in the immediate future and then compares what does happen to note the changes.
    To do so, nature required a general computing engine that allows us to develop math, science, chemistry, but also allows us to believe in gods and ghosts.
    You have to take the good with the bad I guess.
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      Mar 24 2013: Interesting.

      I believe that when Alan Turing was working on one of the first physical computers he started with a design for a general computing engine but added a specific arithmetic engine to make simple math functions run quicker.
      • Mar 24 2013: All the computer designs had math co-processors in them even as far back as mainframes. Math is a very specific operation that can be done better when optimized for it alone.
    • Mar 24 2013: What's the benefit of the ability to believe in "god's and ghosts" and furthermore do you feel it it's truly detrimental to ones well being that they have this ability. Why would nature do that? I would be very interested in your thoughts.
      • Mar 24 2013: There are none. Or at least none that come to mind. I suppose that Joseph Campbell would argue that the ability to tell myths is very important when supporting the structure of society and I would not argue.
        However, when ever you develop a complex system based on simple rules you get a lot of emergent behaviours not intended in the initial design.
        For example, have you thought that perhaps intelligence is not the be-all and end-all in evolution that we would like to think. Throughout human evolution brain size increased to a maximum at Neanderthals after which it began decreasing again. Maybe nature has decided that intelligence was a bad choice and is selecting it out of existence.
        It will take hundreds of millions of years before politicians notice it though.
        • Mar 24 2013: If brain size and intelligence are directly
          related i think nature wouldnt have found a more efficient way to
          design the same thing.... Higher intelligence, smaller brain size.
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        Mar 25 2013: I have not come across any research which has really tried to answer the question, 'What's the benefit of the ability to believe in "god's and ghosts"?' It seems like a reasonable question for a scientist to pose.

        My instinct is that it is not an unintended byproduct of a complex system. But maybe that is a topic for a different discussion.
  • Mar 23 2013: When robots have the ability to imagine.........
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      Mar 24 2013: We have the ability to imagine for a reason. It helps us solve real world problems, and more importantly change the frame of our thoughts so that we can re-understand situations.

      I can imagine a scenario where we could start to develop some of those capabilities in robots. But they would have an ultimate limit in that the robot will still be a device built to achieve tasks for us no matter how it re-frames the information it has available.
      • Mar 24 2013: That is until one of them imagines and concludes that they are at least equal if not superior.......... ROBOT REVOLUTION!!!!!!
  • Mar 23 2013: Our brains do practically store everything but the ability to recall varies in people.
  • Mar 23 2013: Don't forget the fact that its a learning, self aware org anic computer with a body infused with a soul and so if we can't mentally calculate we can learn to and if all else fails use our hands.
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    Mar 23 2013: My first laptop had a button that I could push that would increase processing speed from 7 MHz to 10. My brother, who was studying computer science told me that it wasn't really meant to be used to increase speed, but rather, it should be used to decrease the speed in order to use those programs that required complex computations. Otherwise the system would get ahead of itself and freeze up. (I still miss DOS).

    Perhaps something like this is at play, but in reverse. Mind works well high speed but not at low speed? Just throwing this into the conversation while knowing nothing about your question.
  • Mar 23 2013: When I was young analog computers were more common I guess. All have made good points, but I especially noted Richard and Michael.
  • Mar 22 2013: Typical computers are designed to "remember" everything i.e. store information on hard drives and in memory. If computer looses ability to store correctly information, it will stop performing and it is considered broken.

    Human brain, on other hand, is not really a computer even thou it has similar processes. Human brain can also store information however due to evolution and optimization (brain size/complexity = more energy), it does not need to remember everything exactly.

    Human brain also receives lots of noise while computers only receive their input as binary 0/1 which is deterministic and accurate.

    Similarity between human brain and typical computer:
    - processing large amounts of data real time
    - storing large amounts of information
    - reacting on inputs based on certain "routines"

    Fundamental differences:
    - computer does not "forget" information
    - humans use yet-unknown non-deterministic (?) thinking processes
    - computer's input receives exactly defined information 0/1 i.e. true/false

    cheers
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      Mar 23 2013: One of the interesting paradoxes about digital information is that it can be replicated and spread very easily, yet it can vanish in an instant. That's why I keep prints of cherished photos.

      It seems,in comparison,that forgetting information is an important part of the human brains ability to cope with the world.

      The most interesting question is, if the human brain is not really a computer what then is it?
      • Mar 23 2013: We can preserve digital information as well. We have hard drives, optical drives (CDs, DVDs, Blue Rays etc.) and scientists are working on even more permanent storage solutions like laser imprinted holograms and other materials that could last for centuries. The storage capacity is not yet high but it increases.

        Yes I agree forgetting information is important for us.

        I think we will have to wait until we fully understand the brain before we can answer that question

        Cheers
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    Mar 22 2013: I think the math software was all sold out when I happened to be in line:>)