Species Brain Weight as % of Body Weight human 2.10 bottlenose dolphin 0.94 African elephant 0.15 killer whale 0.09 cow 0.08 sperm whale (male) 0.02 fin whale 0.01
I stand corrected. I meant simple groups, of course.
However, you misunderstand my point. I am not criticizing anyone for lack of precision.
I was pointing out the disparity between the idealized perception of math and the way it is practiced in real life. Most mathematical reasoning relies on certain intuitions and common
knowledge. It would be virtually impossible to take a modern math paper and reduce it to axioms.
Therefore math that is practiced is not the Platonic perfect math, but rather a social math
based on certain social conventions and beliefs.
It is interesting to notice that
judging the importance of problems in math is also a very social, largely determined by a few well-established experts.
I think as a mathematician (or a future mathematician) you would do well to
think these issues through.
I'll grant there is a finite probability of error, but it's about as probable that the classification of finite groups is wrong as it is that I am actually typing this from another planet via the soon-to-be-discovered Aethernet.
On what grounds do you make this statement? I know that some experts in the field have serious doubts as to the completeness of the classification of finite groups. Just because each paper was peer reviewed does not mean a thing. Some of those papers are well over 100 pages long and very dense.
I agree with you as far as the weaker statement is concerned. There are statements in math which follow from the axioms beyond doubt. Same cannot be said about sciences.
It is one of my pet peeves how mathematicians like to exaggerate the objective side of math though:)
How silly. The solution is simple:
Start by proving that a particular machine is capable of evaluating proofs for truth....
There actually are programs out there now which can be used to describe proofs in a computer-readable language and which are consequently capable of verifying that a proof is accurate.
Nothing is simple...
That is fine and dandy in theory. However building a machine capable of evaluating a
a real mathematical proof as found in math papers seems far harder then checking the proofs manually.
Of course, you can always build a simple (or sophisticated) logic checking device but that has little to do with the way people do math in real life.
A mathematical proof is an absolute certainty. Note that I am not claiming that the underlying axioms are certain. I am only claiming that the proof itself is certain.
To put it another way, mathematicians are never certain about their underlying axioms but they are absolutely certain that if those axioms hold then the result stated in the proof also holds. It's kind of like a building with indestructible walls but no foundation.
This statement is a misconception that mathematicians enjoy to perpetuate.
The proof in modern math is rarely an absolute certainty and almost never starts with axioms.
One striking example is classification of finite groups, which is estimated to be spread over around 10000 papers in various journals. Can a single person or even a small group of people read it and say with absolute certainty that there are no errors?
How can someone be certain that a proof contains no errors? Presumably, by reading it carefully and checking all the steps. However, unless the theorem is very simple, there is always a chance of missing something important. One might argue that a group of people going over the proof several times can make a judgement about its veracity. True, but it is a purely probabilistic
statement, which is hardly satisfactory.
Ah, good ole Catastrophe Theory. Rene Thom was certainly a first-class mathematician but his applications were a bit on the weird side.
Not that Wolfram's applications are all that convincing. Except for cool patterns on seashells
he does not seem to have anything particularly impressive. In fact he fails to solve any problem physicists might care about.
The notion of irreducible complexity also seems to miss out, most phenomena are, presumably, irreducibly complex and yet there are things to say about them.
Re:It's like Netscape v. Microsoft in that...
on
Google v. Microsoft
·
· Score: 4, Informative
Noteably, this includes web searches, which is really just a problem in graph theory.
Not at all. The graph theory is important, of course, but web searches involve the following:
1. You have to find the right metric in which to measure the success of your search. The metric is determined by what people want to find. The graph theory is a way to formalize whatever intuition you might have about it.
2. You have to be able to find the results and to deliver them quickly. That's a complex implementation problem.
Graph theorey is no more than a small part of what's involved.
What's wrong with a 4-wheel drive car, say Volvo or Subaru? It has just as much traction and is far less likely to tip over.
I've was in a Jeep Cherokee once, when the driver, my friend, overestimated his car and his driving skill and spinned on a snowy road and went straight into a ditch. Amazingly, the thing did not roll, but it was stuck there for good, 4-wheel drive or not.
Although can I just say that I hate the word monetize? As in, "This allows us to monetize our content." I don't want to buy anything from anyone who monetizes. Please, just use "sell".
Why, monetize and sell have different connotations. Monetize means that you are converting something into money.
From the Oxford Dict.: b. To convert (an asset, debt, etc.) into money, to realize the value of (an asset, debt, etc.) as currency; spec. to convert (government debt) to a more liquid form, as by redeeming treasury bills or replacing bonds with bills. Also: to assess in terms of monetary value.
Selling is more ambiguous. So in your example they don't want to get rid of their content by selling it, rather, they want to find a way to convert it into a source of revenue.
Personally, for my laptop, I want Intel to use their latest & greatest mobile technology, and then UNDERCLOCK that processor down to 700MHz, buying me more compute time on the road.
That is exactly what happens when you run on batteries, except it underclocks to 600mhz, didn't you know?
Not instantly enough to be published in four(!)
journals first;)
In any case, it goes to show that the difference between science and humanities, as far as the standard of proof is concerned, might not be as big as we imagine.
I remember reading some article recently, where the author seriously claimed that physicists were smarter than humanities people, since few humanities French lit. Ph.D.'s would be able to get a Ph.D. in physics, while a physicist would have no difficulty obtaining a Ph.D. in French lit. A laughable assertion.
Apparently a scientist with not much training in "deconstructionism" can write a whole load of baloney and get it published in a journal. (See first +5 post of this article for the link, etc. etc.) The reverse could never happen.
Ah, but the reverse did happen. Brothers Bogdanov published some physics paper in fairly well-established journls which are apparently nonsencial.
Do a search for Bogdanov hoax and you will find it.
Slashdot Mirror
Here is an interesting table:
n .h tml
Species Brain Weight as % of Body Weight
human 2.10
bottlenose dolphin 0.94
African elephant 0.15
killer whale 0.09
cow 0.08
sperm whale (male) 0.02
fin whale 0.01
http://dubinserver.colorado.edu/prj/jbes03/brai
However, you misunderstand my point. I am not criticizing anyone for lack of precision. I was pointing out the disparity between the idealized perception of math and the way it is practiced in real life. Most mathematical reasoning relies on certain intuitions and common knowledge. It would be virtually impossible to take a modern math paper and reduce it to axioms.
Therefore math that is practiced is not the Platonic perfect math, but rather a social math based on certain social conventions and beliefs.
It is interesting to notice that judging the importance of problems in math is also a very social, largely determined by a few well-established experts.
I think as a mathematician (or a future mathematician) you would do well to think these issues through.
On what grounds do you make this statement? I know that some experts in the field have serious doubts as to the completeness of the classification of finite groups. Just because each paper was peer reviewed does not mean a thing. Some of those papers are well over 100 pages long and very dense.
It is one of my pet peeves how mathematicians like to exaggerate the objective side of math though :)
Nothing is simple...
That is fine and dandy in theory. However building a machine capable of evaluating a a real mathematical proof as found in math papers seems far harder then checking the proofs manually.
Of course, you can always build a simple (or sophisticated) logic checking device but that has little to do with the way people do math in real life.
It is quite obvious to me that the Earth is motionless and the Sun rotates around the Earth. Seems like a nice simple theory.
The point is, what is "obvious" and "simple" depends a lot on what you think and what you know and is by not necessarily universal.
This statement is a misconception that mathematicians enjoy to perpetuate.
The proof in modern math is rarely an absolute certainty and almost never starts with axioms.
One striking example is classification of finite groups, which is estimated to be spread over around 10000 papers in various journals. Can a single person or even a small group of people read it and say with absolute certainty that there are no errors?
How can someone be certain that a proof contains no errors? Presumably, by reading it carefully and checking all the steps. However, unless the theorem is very simple, there is always a chance of missing something important. One might argue that a group of people going over the proof several times can make a judgement about its veracity. True, but it is a purely probabilistic statement, which is hardly satisfactory.
So who decides which theory is "simpler"?
Not that Wolfram's applications are all that convincing. Except for cool patterns on seashells he does not seem to have anything particularly impressive. In fact he fails to solve any problem physicists might care about.
The notion of irreducible complexity also seems to miss out, most phenomena are, presumably, irreducibly complex and yet there are things to say about them.
Not at all. The graph theory is important, of course, but web searches involve the following:
1. You have to find the right metric in which to measure the success of your search. The metric is determined by what people want to find. The graph theory is a way to formalize whatever intuition you might have about it.
2. You have to be able to find the results and to deliver them quickly. That's a complex implementation problem.
Graph theorey is no more than a small part of what's involved.
Well nothing is really wrong, except that the old method seems a lot simpler!
That was meant to be humorous, right?
If only I could find a cheap and easy way to produce money...
I've was in a Jeep Cherokee once, when the driver, my friend, overestimated his car and his driving skill and spinned on a snowy road and went straight into a ditch. Amazingly, the thing did not roll, but it was stuck there for good, 4-wheel drive or not.
And you sold those things to them, right?
Right, my point is that being tall does not necessarily imply that you cannot move fast.
I am not saying that you have to be as fast as MJ, of course.
Hm... I've heard Michael Jordan was pretty tall too.
Right. According to a new survey of internet users, more than 50% of the surveyed lie on their survey questions.
Why, monetize and sell have different connotations. Monetize means that you are converting something into money.
From the Oxford Dict.:
b. To convert (an asset, debt, etc.) into money, to realize the value of (an asset, debt, etc.) as currency; spec. to convert (government debt) to a more liquid form, as by redeeming treasury bills or replacing bonds with bills. Also: to assess in terms of monetary value.
Selling is more ambiguous.
So in your example they don't want to get rid of their content by selling it, rather, they want to find a way to convert it into a source of revenue.
Personally, for my laptop, I want Intel to use their latest & greatest mobile technology, and then UNDERCLOCK that processor down to 700MHz, buying me more compute time on the road.
That is exactly what happens when you run on batteries, except it underclocks to 600mhz, didn't you know?
In any case, it goes to show that the difference between science and humanities, as far as the standard of proof is concerned, might not be as big as we imagine.
I remember reading some article recently, where the author seriously claimed that physicists were smarter than humanities people, since few humanities French lit. Ph.D.'s would be able to get a Ph.D. in physics, while a physicist would have no difficulty obtaining a Ph.D. in French lit. A laughable assertion.
Ah, but the reverse did happen. Brothers Bogdanov published some physics paper in fairly well-established journls which are apparently nonsencial.
Do a search for Bogdanov hoax and you will find it.
That service is a $20 option.
Use your head (if you got one, that is) before you call people names.
A patient who had never been sick?