Originally posted by: loki8481
I think the OP is running on a single P1 100MHz
Originally posted by: loki8481
I think the OP is running on a single P1 100MHz
Originally posted by: vital
do you know how fast a 100MHz cpu can calculate numbers compared to a human brain? there is no comparison.
Originally posted by: vital
do you know how fast a 100MHz cpu can calculate numbers compared to a human brain? there is no comparison.
Originally posted by: loki8481
I think the OP is running on a single P1 100MHz
The Math Instinct by Keith Devlin
CAN dogs do calculus? Well no, not the way college students do it. For one thing, dogs usually get the right answer. When chasing a ball thrown into a lake, dogs run along the beach and then choose just the right point to jump into the water to reach the ball in the shortest time. To solve this problem on paper takes time and calculus, but canine brains seem to work it out swiftly and instinctively.
Keith Devlin asserts that there are two kinds of maths: natural and symbolic. Natural maths has evolved over millions of years, giving both animals and humans incredible mathematical abilities, each linked to specific survival needs, such as navigation or catching prey. Symbolic maths is unique to humans and is at most 3000 years old. Our brains have not had time to evolve specialised structures to perform symbolic maths, so we have to co-opt abilities that evolved for other purposes. He argues that this is why so many people struggle with the abstract rules they are required to learn at school.
Devlin spends the bulk of The Math Instinct describing the hard-wired abilities of animals. The Tunisian desert ant finds its way around by dead reckoning, which requires precise measurements and computations. Lobsters can navigate by sensing the Earth's magnetic field as accurately as if they were connected to the GPS network.
If animals can achieve all this, why does the average human have so much trouble with arithmetic? According to Devlin, we don't, as long as it relates to a concrete problem, such as picking the best buy at the supermarket or giving the correct change. But devoid of context, the rules for manipulating symbolic representations of numbers make little sense to most people, who begin to make mistakes they never would while shopping.
How does Devlin's research help in the classroom? I did rather wonder. We do not want our students feeling inferior to lobsters. Fortunately he ends on a positive note. If you understand how symbolic concepts connect to the natural maths you can already do, then it all boils down to practising until those abstract rules take on a more concrete reality in your mind. Back to those times tables, then.
From issue 2494 of New Scientist magazine, 09 April 2005, page 47
Originally posted by: So
quoted from New scientist, since it requires a subscription:
The Math Instinct by Keith Devlin
CAN dogs do calculus? Well no, not the way college students do it. For one thing, dogs usually get the right answer. When chasing a ball thrown into a lake, dogs run along the beach and then choose just the right point to jump into the water to reach the ball in the shortest time. To solve this problem on paper takes time and calculus, but canine brains seem to work it out swiftly and instinctively.
Keith Devlin asserts that there are two kinds of maths: natural and symbolic. Natural maths has evolved over millions of years, giving both animals and humans incredible mathematical abilities, each linked to specific survival needs, such as navigation or catching prey. Symbolic maths is unique to humans and is at most 3000 years old. Our brains have not had time to evolve specialised structures to perform symbolic maths, so we have to co-opt abilities that evolved for other purposes. He argues that this is why so many people struggle with the abstract rules they are required to learn at school.
Devlin spends the bulk of The Math Instinct describing the hard-wired abilities of animals. The Tunisian desert ant finds its way around by dead reckoning, which requires precise measurements and computations. Lobsters can navigate by sensing the Earth's magnetic field as accurately as if they were connected to the GPS network.
If animals can achieve all this, why does the average human have so much trouble with arithmetic? According to Devlin, we don't, as long as it relates to a concrete problem, such as picking the best buy at the supermarket or giving the correct change. But devoid of context, the rules for manipulating symbolic representations of numbers make little sense to most people, who begin to make mistakes they never would while shopping.
How does Devlin's research help in the classroom? I did rather wonder. We do not want our students feeling inferior to lobsters. Fortunately he ends on a positive note. If you understand how symbolic concepts connect to the natural maths you can already do, then it all boils down to practising until those abstract rules take on a more concrete reality in your mind. Back to those times tables, then.
From issue 2494 of New Scientist magazine, 09 April 2005, page 47
In some senses it is very helpful to compare the brain to a CPU and think of it like a processor.
But examined in detail this is not always helpful, because the algorithms the brain uses for "processing" information are not performed like those of a CPU.
Specifically the brain uses highly parallel methods for nearly all lower level thinking. The closest thing that a brain has to a "cycle" is the time it takes for a synapse to fire, but since this doesnt happen in series, it isnt very cyclical.
An interesting sidenote: it has been learned that the human mind is able to perform visual recognition tasks in times as short as 1/20 of a second. Based on synapse firing times, it has been determined that this leaves time for no more than 100 steps in a neural-net sequence. This has been labeled the "100 step rule."
Compare this to the way we would teach a computer to perform a visual recognition task: scan the entire image, performing complex edge detection routines. Using this information, determine those feature which are typically part of larger scale stuctures. Then perform a statistical analysis of these features to determing if they appear in a likely "constellation." This entire algorithm may contain many millions of sequential steps.
The brain < 100 steps
A CPU > 1000000 steps (maybe closer to 1000000000 for a really accurate routine...)
This just gives you an idea of how differently the brain operates from a CPU. The amazing thing is that we are starting to build CPU's that can compete on the same time scales as the brain, doing things sequentially.
Hopefully neuroscience will advance in the next few decades to the point that we really understand what is going on in the brain to the point that we can implement it in machines. I want to be alive to see it...

 
				
		