How Mathematics Can Make Smart People Dumb
- Thread starter cancel2 2022
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cancel2 2022
Canceled
I can't imagine that many would read it to the end except for you and maybe Watermark.
Why, because you think we other less smart females and males won't "get it", thanks, I am really, thanks. Sheesh...
cancel2 2022
Canceled
I just imagined that most people would find it boring unless they are interested in maths.
I did read it and I think this gentlemen would be a good teacher. My math interest, music.
Thanks for the clarification, I should have used a winking happy face. I didn't mean to be harsh.
Bfgrn
New member
Why I Am Not an Austrian Economist
Mathematics, Econometrics, and the Progress of Economics
More than anything else, what prevents Austrian economists from getting more publications in mainstream journals is that their papers rarely use mathematics or econometrics, research tools that Austrians reject on principle. They reject mathematical economics on principle because of the assumptions of continuity and differentiability
Mathematics, Econometrics, and the Progress of Economics
More than anything else, what prevents Austrian economists from getting more publications in mainstream journals is that their papers rarely use mathematics or econometrics, research tools that Austrians reject on principle. They reject mathematical economics on principle because of the assumptions of continuity and differentiability
Mott the Hoople
Sweet Jane
One of the most common errors in applied mathematical analysis is to fail to notice when a mathematical argument proves too much. This occurs when the same argument can be deployed more generally than in the particular case being considered, and in other cases where it can be deployed it leads to conclusions that are clearly absurd.
I can relate to this from personal experience. I was once managing a Superfund Project. We were testing a high temperature process which would incinerate organic toxins (reduce them to CO2 and H2O) and would react inorganics into chemically inert compounds. To verify that this process worked we had to create a statistically representative sampling plan and then test all sample using a US EPA Toxicity test. These test use very sophisticated instruments call a Gas Chromatograph/Mass Spectrometer (GC/MS) which can measure organics in the parts per billion range and a an Inductively Coupled Argon Plasma Spectrometer (ICP) which can measure inorganics/metals in the parts per billion range. This US EPA toxicity test tests for 43 common industrial toxic (Arsenic, Mercury, Lead, 1,1,1-Trichloroethlyene, Benzene, etc,.). We tested in the order of 20 samples per our sampling program. All 20 sample came back with all 43 toxins measuring below instrument detection limits. Which pretty much means those 43 toxins were not present in all 20 some samples.
When I presented that information to the general contractor representing the US Air Force their representative asked me. How do I know this information is significant? To which I replied, because all the data complies with the data quality objectives of our sampling plan and and the sampling plan is statistically representative based on the "XYZ" formula we used. The Rep then said to me "No, that's not what I mean. How do I know that these toxins couldn't end up in your product at some time?". To which I replied, using common sense "Cause if it aint there, it aint there!". To which he said "How so?". I said "look at the data. Nothign was detected!" and he replied "But what's the probability that something could be detected?"
By this time I was getting upset so I said to him. Look if any data population set or a sample of that population set has no standard deviation, that is there is no variation in the data, that is proof that the data is statistically significant.
To which he said "How do I know that?"
So I then took my data set. Which was essentially all "0" or nothing. I then calculated a standard deviation, a 99% confidence interval and a Students (t) Test of statisctical significance for nothing.
When I was completed I had succesfully demonstrated that, yes ineed, nothing is significant!
Which fully meets the authors criteria of absurdity stated above. How could nothing be significant?
A perfect case of mathametics making you dumb.
The good news was I spent an entire day calculating that and I charged the general contractor 8 billable hours for it. He wasn't to happy about that either.
I can relate to this from personal experience. I was once managing a Superfund Project. We were testing a high temperature process which would incinerate organic toxins (reduce them to CO2 and H2O) and would react inorganics into chemically inert compounds. To verify that this process worked we had to create a statistically representative sampling plan and then test all sample using a US EPA Toxicity test. These test use very sophisticated instruments call a Gas Chromatograph/Mass Spectrometer (GC/MS) which can measure organics in the parts per billion range and a an Inductively Coupled Argon Plasma Spectrometer (ICP) which can measure inorganics/metals in the parts per billion range. This US EPA toxicity test tests for 43 common industrial toxic (Arsenic, Mercury, Lead, 1,1,1-Trichloroethlyene, Benzene, etc,.). We tested in the order of 20 samples per our sampling program. All 20 sample came back with all 43 toxins measuring below instrument detection limits. Which pretty much means those 43 toxins were not present in all 20 some samples.
When I presented that information to the general contractor representing the US Air Force their representative asked me. How do I know this information is significant? To which I replied, because all the data complies with the data quality objectives of our sampling plan and and the sampling plan is statistically representative based on the "XYZ" formula we used. The Rep then said to me "No, that's not what I mean. How do I know that these toxins couldn't end up in your product at some time?". To which I replied, using common sense "Cause if it aint there, it aint there!". To which he said "How so?". I said "look at the data. Nothign was detected!" and he replied "But what's the probability that something could be detected?"
By this time I was getting upset so I said to him. Look if any data population set or a sample of that population set has no standard deviation, that is there is no variation in the data, that is proof that the data is statistically significant.
To which he said "How do I know that?"
So I then took my data set. Which was essentially all "0" or nothing. I then calculated a standard deviation, a 99% confidence interval and a Students (t) Test of statisctical significance for nothing.
When I was completed I had succesfully demonstrated that, yes ineed, nothing is significant!
Which fully meets the authors criteria of absurdity stated above. How could nothing be significant?
A perfect case of mathametics making you dumb.
The good news was I spent an entire day calculating that and I charged the general contractor 8 billable hours for it. He wasn't to happy about that either.
Mott the Hoople
Sweet Jane
When mathematical arguments prove too much, it is often as a result of faulty assumptions. If an applied mathematical argument leads to a conclusion that is highly counterintuitive, or if the form of argument can be deployed just as effectively to prove other conclusions that are highly counterintuitive, then this is good reason to further scrutinize the assumptions made in the argument.
One should be careful about this paragraph. Though in general principle {emphasis added} I agree with the author and he is correct that a highly counterintuitive conclusion should be thoroughly scrutinized it must also be recognized that many scientific conclusion are indeed counterintuitive.
One should be careful about this paragraph. Though in general principle {emphasis added} I agree with the author and he is correct that a highly counterintuitive conclusion should be thoroughly scrutinized it must also be recognized that many scientific conclusion are indeed counterintuitive.
FUCK THE POLICE
911 EVERY DAY
I've actually seen this article posted on r/economics before, and I posted a criticism of it (although I didn't completely disagree with its main point).
For one thing, it's often easy to "prove too much" in logical arguments as well. For instance, "lower taxes produce more revenue!" In some cases this is true, yes. But, clearly, not in all cases. Unfortunately, this happens to be one of Dixie's favorite arguments, and no matter how many times I point out the error in it, he returns to it anew in the next thread. Like an alzheimers patient who wakes up every day under the impression that they're children and it's Christmas, he treats it as some new wonder he has found.
Another is "it makes no sense to kill people for killing people, therefore the death penalty is wrong!" If you apply this logic everywhere, rather than confining it to the domain of the death penalty, it's wrong to imprison kidnappers as well. What are we supposed to do with them? I suppose that, in an ideal world, we'd just tell them they did a bad thing, they'd immediately repent and never repeat their action, and our failure to mete out retribution wouldn't encourage others to go down the same path. But we do not live in such a world. These are just very shitty arguments for their respective points.
As a second point, in this particular case math is simply being misused. I doubt that the person who drew that poster really understands what it meant, and I doubt they were under the impression that the people who saw it would either. It's point seems to have been "Hey guys, look, this is complicated, therefore I'm right!" Math and science is currently kind of in vogue in my generation. This does have some bad effects. In the early 20th century, science was similarly in vogue, and people had a great amount of faith in it, but little true understanding. This caused them to fall for a lot of charlatans peddling scientific sounding contraptions, for instance, a machine that could diagnose and cure any disease through radio waves. People actually used to buy water infused with radium, and a lot of people drank themselves to radiation poisoning with it. And we had all of these new ideologies, such as Marx's "scientific socialism", which really weren't scientific at all. The ultimate effects weren't really that great for science, because people simply began to have unrealistic expectations and blamed science when the unrealistic expectations weren't met.
Similarly, my generations ignorant faith in mathematics and science leaves them open to arguments like this. In form, it's really more of an argument from authority than anything else. However, I don't think that it's appropriate to use this as a criticism of academic use of mathematics. In a setting where everyone involved understands the mathematics and has the ability to offer criticisms of it, mathematics can be a very effective tool. In a setting like this, it can be seriously misused. Simply stating the practical fact that carbon taxes discourage the use of CO2 would've been a stronger argument for your point, and it would've been understandable. It's a bad approach to simply refuse to believe in anything you aren't capable of fully understanding yourself. That's anti-intellectual hogwash - it's not to be expected that you have PhD level knowledge of every subject, and to refuse to believe in anything that requires such knowledge to fully understand is every bit as foolish as drinking the radium water because the salesman said it was sciency. You simply have to have a good bullshit filter, and make sure that your sources are reliable.
For one thing, it's often easy to "prove too much" in logical arguments as well. For instance, "lower taxes produce more revenue!" In some cases this is true, yes. But, clearly, not in all cases. Unfortunately, this happens to be one of Dixie's favorite arguments, and no matter how many times I point out the error in it, he returns to it anew in the next thread. Like an alzheimers patient who wakes up every day under the impression that they're children and it's Christmas, he treats it as some new wonder he has found.
Another is "it makes no sense to kill people for killing people, therefore the death penalty is wrong!" If you apply this logic everywhere, rather than confining it to the domain of the death penalty, it's wrong to imprison kidnappers as well. What are we supposed to do with them? I suppose that, in an ideal world, we'd just tell them they did a bad thing, they'd immediately repent and never repeat their action, and our failure to mete out retribution wouldn't encourage others to go down the same path. But we do not live in such a world. These are just very shitty arguments for their respective points.
As a second point, in this particular case math is simply being misused. I doubt that the person who drew that poster really understands what it meant, and I doubt they were under the impression that the people who saw it would either. It's point seems to have been "Hey guys, look, this is complicated, therefore I'm right!" Math and science is currently kind of in vogue in my generation. This does have some bad effects. In the early 20th century, science was similarly in vogue, and people had a great amount of faith in it, but little true understanding. This caused them to fall for a lot of charlatans peddling scientific sounding contraptions, for instance, a machine that could diagnose and cure any disease through radio waves. People actually used to buy water infused with radium, and a lot of people drank themselves to radiation poisoning with it. And we had all of these new ideologies, such as Marx's "scientific socialism", which really weren't scientific at all. The ultimate effects weren't really that great for science, because people simply began to have unrealistic expectations and blamed science when the unrealistic expectations weren't met.
Similarly, my generations ignorant faith in mathematics and science leaves them open to arguments like this. In form, it's really more of an argument from authority than anything else. However, I don't think that it's appropriate to use this as a criticism of academic use of mathematics. In a setting where everyone involved understands the mathematics and has the ability to offer criticisms of it, mathematics can be a very effective tool. In a setting like this, it can be seriously misused. Simply stating the practical fact that carbon taxes discourage the use of CO2 would've been a stronger argument for your point, and it would've been understandable. It's a bad approach to simply refuse to believe in anything you aren't capable of fully understanding yourself. That's anti-intellectual hogwash - it's not to be expected that you have PhD level knowledge of every subject, and to refuse to believe in anything that requires such knowledge to fully understand is every bit as foolish as drinking the radium water because the salesman said it was sciency. You simply have to have a good bullshit filter, and make sure that your sources are reliable.
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FUCK THE POLICE
911 EVERY DAY
Now that I read it again, he actually echoes my assertion that it's a bit of an appeal to authority:
Minister of Truth
Practically Perfect
I still have nothing to fear yet, based upon my math skills.
cancel2 2022
Canceled
I think one of the points you can take from the article is the extreme reliance that financial institutions placed on mathematical models and their supposed ability to predict the markets. WE can all how well that's turned out.
FUCK THE POLICE
911 EVERY DAY
Using math to attempt to predict the future is mostly a bad use of math as well. They basically just jumble things together until they get something that vaguely tracks past data and call it a day. It's not an act of ingenuity.
However, as I've often said, economists probably have a lot of good stuff to say, as long as you don't ask them to predict anything. The use of math you've just described really is not a scientific use of math and, again, I don't think it's appropriate to use it as a criticism of math used in an academic setting where all parties have the ability to understand what's being said. Math is just a different language that can often state very concisely what may be difficult to put into words. On the other hand, I've seen people resort to mathematical equations to state something that really did not need them. They do this all the time in my textbooks. It's just obfuscationism.
Really, you can tell the seriousness of a discipline by how often people need to resort to such tactics. When talking about hard engineering, chemistry, and other stuff of that nature, they often have to try very hard to dumb things down in order to make it understandable to the proles. In contrast, other disciplines such as sociology or literary criticism often say the simplest and most obvious things in the world in a thick code that only sounds complicated on the surface.
Minister of Truth
Practically Perfect
Actually, I was reading a similar article recently, arguing that economists have gone too far in the direction of turning their field into an accepted hard science - complete with all of the latest formulas and theorems. These systems were applied all accross our nation's financial markets, leading up to the latest national recession.
Mott the Hoople
Sweet Jane
What math skills? You were a history major.
Minister of Truth
Practically Perfect
What math skills? You were a history major.
Well, now you know why. I'm studying a bit, and my friend is promising to tutor me. One day I would like to persue a degree which requires at least some math, such as an MBA (business programs require precalculus these days).
Mott the Hoople
Sweet Jane
Yes, some integral calculus and a whole hell of a lot of statistics. Probably management science too which is really a math class. I took those in my masters program.
Just remember this to keep motivated when you're struggling and working to learn maths. The ulimate purpose of math is to get you (3D) laid. For each new significant and substantive maths skills you learn you make your self more marketable. With greater marketability come greater economic prosperity. With greater economic prosperity comes women.