On the normative use of mathematics in economics as a rhetorical device for persuasion based on the logical fallacy of appeal to authority not supported by context.
Mathematics never says anything about the state of the world because it is about abstract relationships, but it can be used to appear to do so when accompanied with handwaving. But only testing can determine whether abstract relationships are actually the case.
Consistency does not implies correspondence. That's why we do science. But the math must be consistent. And in economics, this implies stock-flow consistency, which econometric models do not always observe.
Real-World Economics Review Blog
It’s the math again
David Ruccio | Professor of Economics, University of Notre Dame
I'll throw out two metaphors that dont have any mathematics in them that are very confused/confusing:
ReplyDeleteKrugman's "Liquidity Trap"
Koo's "Balance Sheet Recession"
Try to think about what these metaphors represent mathematically... you cant do it.
So I dont get it where David here writes:
"My alternative view was that mathematics was just one language among many, and therefore one set of metaphors among many. And like all metaphors, it served at one and the same time to enable and disable particular kinds of ideas."
I dont have any understanding of what this means... I cannot see any similarities between math and metaphors... they are completely different things...
They are separate worlds (to me anyway).. completely different ways of achieving understanding...
What is he trying to say here? People who are non-mathematical can mis-apply mathematics? If this is what he is trying to say I guess I'd agree with him...
rsp,
Matt, if you rephrase those two metaphors ...
ReplyDeleteQuid pro quidity trap,
...and
Balance Sheet Precession
... NOW you got some metaphors! :)
Circle the banks and drain the rubes. It's a classic defensive strategy of all colonialists - whether land-grabbers or Rand-Robbers. Their best defense is now a pretense.
The point that Ruccio is making is that there is a difference between using math as a shell game and as a useful tool in explication of otherwise abstruse material.
ReplyDelete"Liquidity Trap" just means a situation where short term interest rates can't be lowered further, i.e. the 'zero lower bound', and the economy is stuck in a recession or very low growth. People claim it's a 'trap' because further increases in the quantity of base money have no effect or very little effect on demand.
ReplyDelete"Balance sheet recession" just means there is too much private debt.
I don't see why these terms are particularly problematic.
Well Tom the way I often see it is that we have folks who arent really mathematical-type thinkers, who are like 'semantic'-type thinkers, or 'linguistic'-type thinkers who sometimes try to use math to explain their ideas...
ReplyDeleteSo it comes out like 'garbled' or something....
Like Krugman, when you corner him with the math, he'll retort something like: "well thats not the way it works in a 'liquidity trap'.." or something...
What the heck is a 'liquidity trap'? Are we supposed to think of water 'trapped' in a glass? The water cant get out? What does that image have to do with economic policy?
I never understand these metaphors these people come up with...
You have a statement here: "A government that issues its own currency cannot run out of that currency..." There is no metaphor in this statement.... then a moron will repsond: "We'll thats not how MY HOUSEHOLD bank account works!...blah, blah, blah..." thus reverting back to metaphor and throwing out the math (if they ever had it which I doubt...)
We are dealing in systems that are best understood thru mathemetics and unfortunately, a lot of people involved in the analysis at the highest levels imo (I'm not criticizing) dont have the cognitive mathematical ability....
rsp,
y,
ReplyDeleteYou understand them because you have the math to be able to see thru them....
What if you didnt have the maths?
And somebody said "liquidity trap"?
You would think we are 'trapped' or something, no options or something... "we're trapped with no water... ITS A LIQUIDITY TRAP!" or something... like were going to die of thirst?
This is ALL FALSE... rsp
"we're trapped with no water... ITS A LIQUIDITY TRAP!"
ReplyDeleteha ha!
ok.
Metaphors:
ReplyDelete"All the world's a stage,
And all the men and women merely players;"
I get this one! ok!
World= Stage
people= players
ok
trap = ????
liquidity = ????
balance sheet = ????
recession = ?????
I dont get these... rsp,
Matt, the other thing is that people who really understand math, the math and physic PhD's often way that economists don't really understand math, even the best of them. :o
ReplyDeleteMathematics is descriptive, but not always elegant. If I want to describe the properties of fiat, I use words. If I can't use words, I use pictures or charts. Equations are a last resort.
ReplyDeleteAre "Liquidity Trap" and "Balance Sheet Recession" misnomers?
ReplyDeleteBob,
ReplyDeletePictures, charts, diagrams are part of math imo... geometry, etc..
I came across this wiki page on "Mathematical Maturity" that I think gets into what I'm trying to communicate here:
http://en.wikipedia.org/wiki/Mathematical_maturity
rsp,
Bob,
ReplyDeleteI dont even know if they qualify as 'misnomers'...
Krugman I guess is trying to explain something with this metaphor... what it is I have NO IDEA...
What is he saying? 'We're trapped with no liquidity' ? ie "We're out of money!" this is absurd...
Koo: "balance sheet recession"
ok, I know what a balance sheet is
ok, I know what a recession is...
Where is the explanatory relationship?
Or are these just "terms" they are creating?
I look at them as metaphors but the equivalence implied in metaphorical language seems to be missing...
rsp,
Like Krugman says "We're in a liquidity trap!"
ReplyDeleteThere is the metaphor "we're up a creek without a paddle!"
I could break down the latter here but not the former...
rsp,
Matt,
ReplyDeleteSome of those bullet items could be characterized as critical thinking skills.
Charts and diagrams attempt to communicate information visually. Their reliance upon geometry is incidental. Not everyone wishes to see the universe as a set of numbers and equations on a white background.
http://en.wikipedia.org/wiki/Liquidity_trap
ReplyDeleteWords are symbols (containers) that mask meaning. Maths is just another language. A whole bridge can be described physically in one formula; but not what it means to people, and its significance to them.
ReplyDeleteMeaning masks significance (purpose). Meaning can be hidden, revealed, or misrepresented by words because of significance.
Hence: 'look at what they do, not what they say' ...
Feeling is universal knowledge that doesn't need words and is the path to 'insight'. I think it was Beethoven who through insight heard a whole symphony within, and wrote it down in lineal fashion in music symbols.
All education should lead to insight, I believe ....
This comment has been removed by the author.
ReplyDeleteFor a layman like me, it seems undeniable that there are good reasons to be skeptical about the hyper-mathematization of economics. Smith did a good job pointing at them and even Krugman has mollified his original position.
ReplyDeleteWhat I fear is that among those legitimately pushing for a less mathematized economics there are many who want a reason-free economics: one where A and Not A are true at the same time, provided one can write down a convoluted argument, peppered with unintelligible jargon and glib remarks, to "prove" it.
People not too different from Stanley Fish (about whom a recent comment appeared in the New Republic), if one thinks about it:
Stanley Fish Turned Careerism Into a Philosophy
http://www.newrepublic.com/article/114224/stanley-fish-careerism
Maybe you guys should check the net about the so-called Alan Sokal Affair.
jr,
ReplyDeleteI dont see math as 'another language' I see language and math as two separate things... they perhaps end up performing the same function (perhaps 'understanding'?) but in different ways...
Bob,
"Their reliance upon geometry is incidental."
I dont see it as incidental... they are part of it... iow the reason we study geometry is so we can use it in diagrams and charts and so forth... to convey information with the intent to help others reach an understanding...
Larger Point: I dont think we math types are doing a good enough job in understanding what non-math types are going thru, ie the difficulties that non-math people have in reaching an understanding of concepts that are best understood via math...
Imagine trying to communicate to a construction company the detailed design of a large bay spanning bridge using only words... forget it!
I dont know how your all's brains work, but when I read this that Tom wrote some years ago which is now in Warren's 'required readings':
"When banks create money by extending credit (loans create deposits), this occurs completely within the banking system and results in a liability for the bank (the deposit) and a corresponding asset (the loan). The customer has an asset (the deposit) and a corresponding liability (the loan). This nets to zero."
When I read this, in my mind, I can "see" a general ledger system in my mind, with left and right columns, one ledger for each of the two entities mentioned and I can literally "see" the dual, offsetting entries being made in each of these two general ledgers that 'net to zero' as Tom describes IN ONLY WORDS here...
I dont think a majority of human's brains work thru this the way my brain does... ie by actually 'visualizing' a general ledger system in their minds...
most people imo have to "memorize the words for next time it comes up in conversation" but they DONT REALLY UNDERSTAND IT ... because to really understand it (NOT just memorize it!), you have to have the ability to visualize a general ledger system in your head and they dont have this...
So if we dont start to try to really understand what these people are going thru with this subject, we are NEVER going to get thru to them...
We will just continue to accuse them of "fraud" or "conspiracy" or "neo-liberals" or whatever... that is not what is going on...
what is really going on is they lack certain mathematical cognitive abilities and we are not understanding this about them...
rsp,
The purpose of most charts and graphs is not to demonstrate the usefulness of geometry. Nowadays software does the work of ruler and compass, and maintains proper ratios for displaying each variable.
ReplyDeleteVisual displays of information have their own problems due to the way humans process visual input. Flannery Appearance Compensation is an example of this. It uses mathematical equations that the end user never sees. The fact that some symbols were 'compensated' is not explicitly divulged to the end user.
Not sure if what Tom wrote requires knowledge of ledgers. If you haven't seen a (bank) ledger your conception of one may be a stumbling block.
Bob,
ReplyDelete"Visual displays of information have their own problems"
Bob,
"The purpose of most charts and graphs is not to demonstrate the usefulness of geometry..."
That's not what I said... I assert that the reason we study geometry in math curriculum is to ultimately be able to use it to communicate with it... ie with diagrams, angles, dimension drawings, etc...
And, I personally have NO PROBLEM with visual displays of information.... NONE whatsoever.
In fact, I PREFER such depiction of information, rather than words...
However I realize that I may not be like most people in this regard... if you can see my point here...
rsp,
Math is a subset of formal logic. The different branches of math and formal logic are frameworks of formal language. They say nothing about the world, i.e, how things stand. They are about quantitative relationships that can be interpreted semantically, e.g., in counting things. There are rules for semantic interpretation, too. No adding "apples and oranges," for instance.
ReplyDeleteMatt,
ReplyDeleteGeometry was not helpful in helping me communicate visually. Drafting, graphic arts, and cartography are more applicable.
I dont see math as 'another language' I see language and math as two separate things... they perhaps end up performing the same function (perhaps 'understanding'?) but in different ways... [MattF]
ReplyDeleteYes, probably should have said 'maths is just another set of symbols'.... leading to meaning and embodying significance.
What fascinates me about mathematics is its universality (along with colour). From one unified source of energy emerges differentiated streams of energy, whose relations and subsequent forms can be described mathematically, and are reflected in colour and sound. But as I said in different words (symbols) above, different energy streams can be 'felt' and feeling leads to a deeper understanding than thinking. Well, that is my pov. (OMG - pov is a part of poverty)! I wonder what I mean ....:-)
Words, words, words .... truncated worlds! They are too easy to play with; which is where nature's mathematics at least describe without bias, simple conditional existence.
What do we want: feel the sunrise or describe it with maths? Both are useful, but cannot be done together. I believe we have to explore the feeling side of consciousness, at least as deeply as we explore the maths! There are more answers within us than mind could shake a stick at ....
Well jr I think some of us perhaps are created just to enjoy the sunrise and others to not just enjoy it but also seek to understand it...
ReplyDeleteHere is Galileo from the wiki page on Mathematics:
Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."
So to your point jr, looks like Galileo looked at math as a type of 'language' also... you have good company!
But I'm still not 100% convinced that mathematics is just another form of what we normally think of as 'language'.... I see them as two separate concepts that many people have trouble traversing between...
"I dont see math as a subset of language"
right here in this sentence, I've written 'language' (English) BUT, I used 'math' when I write the word 'subset' here... the concept of a 'subset' is separate from the language I use.. for someone to understand my 'language' here, they have to understand the mathematical concept of a 'subset' also...
This is the type of thing I'm talking about with those who remain out of paradigm, we can write all the words/language we want, but if those on the other end of those words do not have the math required for true understanding, its like our words are falling on deaf ears...
rsp,
Matt -- "Or are these just "terms" they are creating?"
ReplyDeleteYes, exactly. These are just terms they have created and defined. They are NOT metaphors. Trying to decipher them as metaphors is not possible, hence your difficulty.
John,
ReplyDelete10-4 I'll try to approach this from a "terminology" standpoint then... interesting...
rsp,
'... I see them as two separate concepts that many people have trouble traversing between... ' [MattF]
ReplyDeleteI find this interesting too Matt.
If I place in your mind the word "triangle" then this may trigger a whole host of meaning to you and significance. If I place in your mind a picture of a triangle, will your meaning and significance be any different?
If I am in a helicopter looking down on London, and my co-pilot happens to have perfected mind control and places in my mind an aerial view of New York, what am I looking at.
Odd example I know, but the point is we 'see' whatever is in our mind. That aspect of human behaviour we call economics has as widely a divergent 'aerial' view.
I have never met MattF but if I saw him for the first time, would I look at him with the eyes of a child, just seeing, without making judgements in my mind. Or would I see through the filter of mind?
So for understanding to happen we need to be able to replicate in the minds of others, through the use of words, images, smells, tastes, sounds, mathematics, colour (i.e. symbols) exactly the same meaning and significance we wish to convey. Mind then (if it is clear and not full of all of its own emotional-mental filters and blenders) becomes the sixth synthesising sense and insight the seventh 'seeing' sense. Behind them all is the entity who either transmits or receives (dependent on the functionality of the organs of perception). So we have the field of knowledge, the organs of knowledge, and the knower. [Patanjali]
In parallel and significant to me, the heart cares naught about all of this. The heart just wants to be fulfilled.