tag:blogger.com,1999:blog-6837159629100463303.post4430288546829992767..comments2021-06-06T04:40:59.126-07:00Comments on Information Transfer Economics: What mathematical theory is forJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-6837159629100463303.post-45470574550787732462017-07-25T01:18:06.121-07:002017-07-25T01:18:06.121-07:00About 40 years ago I implemented a simple A/D conv...About 40 years ago I implemented a simple A/D converter to obtain a digital signal suitable for transmitting a speech signal over a digital channel.<br />This solution was known as "Adaptive delta modulation" although at the time I was not aware that it was already invented some years earlier.<br />https://en.m.wikipedia.org/wiki/Delta_modulation<br />In my solution, the number of transitions in the digital signal was counted and averaged over a certain time and used as the varying step in a second feedback loop which tried to set the transition density to about 50% average. It worked wonderfully.<br />With no analogue input signal the result is highly ordered digital signal with 100% transition density, a simple continouous square wave where the stepsize is minimal.<br />With a very big input signal the stepsize is maximal but insufficient and then the transition density tends to approach 0%, essentially also a square wave signal because it is in fact the clipped input signal.<br />In these extreme situations the digital signal is highly ordered and has a low entropy and no interesting information other than about the presence of an input signal. Whether or not the higher entropy at 50% transition density represent interesting information is quite another matter.Bert Morrienhttps://www.blogger.com/profile/09861280123394845524noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-67203312429161184552017-07-24T11:15:23.731-07:002017-07-24T11:15:23.731-07:00Thanks Tom!Thanks Tom!Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-30073107884611878752017-07-24T10:29:12.278-07:002017-07-24T10:29:12.278-07:00I really enjoyed this one Jason!I really enjoyed this one Jason!Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-74275653401623069412017-07-20T11:08:57.890-07:002017-07-20T11:08:57.890-07:00The realism of the assumptions is a side question....The realism of the assumptions is a side question. If unrealistic assumptions produce empirically valid models, then great! If realistic ones produce empirically invalid models, then that realism doesn't matter.<br /><br />Does anyone think the assumptions of quantum mechanics are "realistic"? Not really. That's why there's constant attempts at new interpretation. It is counter to our intuition about "realism". But they're empirically accurate, so you kind of have to give up on your human gut feelings about "realism". They are <b>biases</b>. Assumptions are either empirically accurate themselves, or effective (i.e. the theory constructed from them is empirically accurate). The "realism" is unnecessary -- unless you just consider "realistic" to be a synonym with "empirically accurate".<br /><br />In which case: <b>just say empirically accurate.</b><br /><br />However in my experience, the purported replacements are themselves as empirically inaccurate as the assumptions they're trying to replace.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-6429404210720118132017-07-20T11:01:44.710-07:002017-07-20T11:01:44.710-07:00It seems to me that economics is a branch of logic...<i>It seems to me that economics is a branch of logic, a way of thinking; and that you do not repel sufficiently firmly attempts à la Schultz to turn it into a pseudo-natural-science. ... But it is of the essence of a model that one does not fill in real values for the variable functions. [4] To do so would make it useless as a model. For as soon as this is done, the model loses its generality and its value as a mode of thought.</i><br /><br />And that footnote [4] (per my link to the letter above) is referring to this:<br /><br /><i>4. Refers to Harrod's claim that the substitution "of real equations for the present empty forms" would bring economics "on its way to looking much more like a mature science" (Harrod 1938:15 , p. 401).</i><br /><br />It's really hard to read this any other way. But maybe Keynes just meant that Roy Harrod shouldn't fill in the values because he was bad at math or something.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-72749183468420518122017-07-20T02:20:01.924-07:002017-07-20T02:20:01.924-07:00"Their only constraint on the math they use i..."Their only constraint on the math they use is showing that their equations are indeed useful ‒ by filling in the values and comparing to data."<br /><br />Here is one economist that tries to follow this approach.<br /><br />“Neoclassical economics turns out to be the one school of thought within the discipline of economics, indeed one of the very few intellectual disciplines in general, that rejects the inductive approach favoured by scientists, and prefers deductivism. It must be considered a unique phenomenon in the history of thought that the originally marginal and eccentric deductive approach to economics has today become the mainstream school of thought. Unhindered by economic reality, deductive economists can start with their preferred axioms, which do not need to be supported by facts – such as the axiom that individuals only care about the maximization of their own material benefit. Additional unrealistic assumptions produce the theories that are so removed from reality. While this is certainly allowed and may be useful as an exercise in logic, the theories, which are specific to the hypothetical environment created by the assumptions, are then used to advance policy recommendations. By this stage, no further mentioning is made of the assumptions necessary for the validity of the argument. The jump from the theoretical and hypothetical models to actual, supposedly workable policy advice is not usually explained. It is striking how seamlessly neoclassical economists have bridged the gap from their wholly fictional world of unrealistic models to recommendations of policies that actual politicians are supposed to implement in reality."<br /><br />R.A. Werner: New Paradigm in Macroeconomics.Postkeyhttps://www.blogger.com/profile/11747509012748106827noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-37900492152390585122017-07-19T22:00:34.022-07:002017-07-19T22:00:34.022-07:00"Keynes was wrong when he said that one shoul..."Keynes was wrong when he said that one shouldn't fill in values in the equations in a letter to Roy Harrod."<br /><br />A bit lazy to look at the history of the conversation but IIRC, Keynes wasn't against modeling per se but using it inaccurately. Ramananhttps://www.blogger.com/profile/11123448543333785121noreply@blogger.com