I've been kicking an idea around after a prolonged argument with a friend about math in economics; why hasn't anyone tried to invent a new type of math specifically designed around the idea of capturing the cause and effect and unidirection nature of time as seen by humans? In physics apparently the equations work no matter which way time runs, one of the reasons the equations aren't applicable in economics is because even if you grant an entirely deterministic and predictable we just can't get the information necessary to predict it on a practical level. So why not alter the math? Why not a new form of math in which all factors have a time index and causal component. Nothing with a time index of t could be said to affect or cause anything with a time index of <t, and then throw some 'art' in in terms of some kind of measure as to how much this affects that.
So say you take Total Savings (TS) as a metric. It gets a subscript 't' and 'c'. Technically people are as much a part of causing the metric as they are of reacting to it if they even do, but they can't react to what they haven't created yet, so a measure of TS at time t can't affect behavior at any time index of >t, and the 'c' could include some guess as to how much TS reacts with or 'causes' other metrics in the market to shift. And, get rid of the equals sign. Replace it with an arrow; this leads to that.
This obviously isn't science, but instead of dismissing math altogether why not try and mold it to something that actually reflects reality to a point? Hell, Austrians could pioneer this kind of thing perhaps. There's already similar types of things done in areas like disease research where cause and effect are important to discern. Maybe someone has already tried this in economics, but I haven't seen it. If any of you have, please point me to it.
xahrx: I've been kicking an idea around after a prolonged argument with a friend about math in economics; why hasn't anyone tried to invent a new type of math specifically designed around the idea of capturing the cause and effect and unidirection nature of time as seen by humans? In physics apparently the equations work no matter which way time runs, one of the reasons the equations aren't applicable in economics is because even if you grant an entirely deterministic and predictable we just can't get the information necessary to predict it on a practical level. So why not alter the math? Why not a new form of math in which all factors have a time index and causal component. Nothing with a time index of t could be said to affect or cause anything with a time index of <t, and then throw some 'art' in in terms of some kind of measure as to how much this affects that. So say you take Total Savings (TS) as a metric. It gets a subscript 't' and 'c'. Technically people are as much a part of causing the metric as they are of reacting to it if they even do, but they can't react to what they haven't created yet, so a measure of TS at time t can't affect behavior at any time index of >t, and the 'c' could include some guess as to how much TS reacts with or 'causes' other metrics in the market to shift. And, get rid of the equals sign. Replace it with an arrow; this leads to that. This obviously isn't science, but instead of dismissing math altogether why not try and mold it to something that actually reflects reality to a point? Hell, Austrians could pioneer this kind of thing perhaps. There's already similar types of things done in areas like disease research where cause and effect are important to discern. Maybe someone has already tried this in economics, but I haven't seen it. If any of you have, please point me to it.
About symbol logic, but probably similar enough.
I have always thought that it isn't really mathematics in general that the Austrian School doesn't approve of for economics, but a specific kind of mathematics (calculus or whatever they try to use). I mean, what's mathematics but a "rigorous" language designed out of a spontaneous order to capture the information on a very low level of analysis? So in principle why wouldn't it be useful to try to build one for economics?
(By the way, I have no idea what you were trying to do in your 2nd paragraph, so I'm just commenting on the general point.)
If I wrote it more than a few weeks ago, I probably hate it by now.
What you described sounds like a variant of temporal logic. Last time I checked there were dozens of varieties, so just shop around. What I do not get, what's wrong with math? By itself, it's just a useful tool, which can of course be abused, but I do not see how math per se is incompatible with praxeology. By math here I mean whatever foundational theory you pick - one of the set theories, category theory, etc. - everything else, like arithmetic, calculus, topology - just builds upon this foundation using definitions.
"(By the way, I have no idea what you were trying to do in your 2nd paragraph, so I'm just commenting on the general point.)" - I, Ryan
That does mess with people. Basically say you want to make the point that is household savings goes up, this will result. When you do that in an equation, what caused what though? I haven't looked at econometric models in years but what I remember is Total Spending equals this plus that minus the other, and in true mathematical form if something changes on on side of the = something on the other must to. Or, maybe more to the point, you take a random walk and you have 8 shcoks with your shock values having a mean of 0. Doesn't that mean the values of the 7 and 8 shocks if known can constrain the prior ones because the mean 'has to be' 0? If so, isn't it a fault in the basic set up that the future can 'cause' the past and that there is no differentiation as to which way time flows?
So say you had some model that said people react to this or that econometric. Aren't they also a part of creating that metric with their own prior behavior to a certain extent? If so, wouldn't their reaction to the metric have to post date any influence they've had on creating it? In physics it's okay because the relations are constant and so it doesn't matter what caused a rock to fall or what not. Knowing enough variables and you can solve for the rest. What we need in economics is a form of math or symbolic logic with some kind of quantitative aspect to it that can differentiate between the ideas of solving to equillibrium vs an actual process which involves moving from one state of being to another and where the past 'causes' the future and not the other way around. Where variables exist as historical data: TS at time index x, x+1, x+2, x+3.... And what data extists at time inex x+50 was caused by what happened at x-x+49, and wil cause what happens at x+51.
So take savings and investment. What if you formulated it as S(1|.8)→I(>1,N) using the format that V(t|c) where V is the variable in question, t is the time factor, c is the causal factor. So the above would mean Savings (S) at time 1 with a measure of causation of 1 and a scale of 0-1, 1 being the highest, leads to Investment (I) at time >1 with no causation running the other way unless you tack something on to investment, then assign a causal rating based on how much influence you think it has on that variable. Or more simply Savings is what leads to Investment in a very direct sense.
More broadly speaking I'm talking about getting rid of the equals sign when time is involved so that the symbols don't describe an equillibrium state but a process that is continual, with equals signs only being used to show concurrent relationships. Something like total income equals total spending might still be applicable. But even those have time elements. So try and get time into the equations not as another variable to be solved for as it is in physics, but as a constraint on what can lead to what and what can cause what. At least this would possibly weed out bad regressions by eliminating certain possibilities.
"What I do not get, what's wrong with math?"
Lack of causation, at least to me that's a big drawback. What 'causes' 4 to equal 2+2? Neither. Raise 4 to 6, you have to somehow add another 2 on to the other side of the equation or it doesn't work. But which came first? Did you make the left side 6, or did you make the right side 2+2+2, or 3+3, or 4+2, or 5+1, or 6+0? In the real world things happen in order, so simultaneous equations don't caputure reality. In reality someone picks up two oranges here, and two at the store, and then puts them together has four. So one side of the equation 'happened' before the other. See what I'm saying?
No in economics I guess people run regressions to see what caused what these days. What I'm saying is what if we try to find a way to formalize ideas concerning what can cause what and how and when? For example, Savings must preceed Investment. And what is invested today must follow some prior act of saving before today.