Proposition of a Mathematical Theorem on Speculative Economy
I had no luck with my previous thread about technological innovation, it got silently deleted. I'm going to try with a new one. I hope Mathematical Analysis and Economy are not banned subjects.
Relevant fact: The sin(x) or cos(x) functions can be accurately approximated using the exponential function.
Proof: FooPlot | Online graphing calculator and function plotter
Theorem: In Speculative Economy, applying Mathematical Analysis to empiric data, the difference between an harmonic oscillation (sin(x) or cos(x)) or an exponential function cannot be determined until half of total investment is gained or lost.
Corollary: This constitutes formal proof that, in Speculative Economy, Mathematical Analysis of empiric data representing oscillations is not the factor determining success or failure in operations. Thus the purpose of existence of Speculative Economy lacks a mathematical basis.
I had no luck with my previous thread about technological innovation, it got silently deleted. I'm going to try with a new one. I hope Mathematical Analysis and Economy are not banned subjects.
Relevant fact: The sin(x) or cos(x) functions can be accurately approximated using the exponential function.
Proof: FooPlot | Online graphing calculator and function plotter
Theorem: In Speculative Economy, applying Mathematical Analysis to empiric data, the difference between an harmonic oscillation (sin(x) or cos(x)) or an exponential function cannot be determined until half of total investment is gained or lost.
Corollary: This constitutes formal proof that, in Speculative Economy, Mathematical Analysis of empiric data representing oscillations is not the factor determining success or failure in operations. Thus the purpose of existence of Speculative Economy lacks a mathematical basis.
The OP needs to do more research the Euler equation as it relates to economics has nothing to do with Euler's formula for the complex exponential expression of sin and cos.
http://mitsloan.mit.edu/shared/ods/documents/?DocumentID=4171
http://mitsloan.mit.edu/shared/ods/documents/?DocumentID=4171
Same here.
OP is under the mistaken opinion that because two "Laws" carry the "Euler" name, are one and the same or at least directly related.
If it were so, then Ohm´s Law could be used to study the French Resistance.
True, it doesn't even need to be printed and handed to banks anymore, a few taps on a keyboard is all that is required
I understand there is a complex form of the exponential function which can produce either the sin(x) or cos(x) functions, or the e^x real exponential.
This does not contradict the fact that the difference between these two extreme cases can be only detected in empirical data after half of total investment has been gained or lost.
Proving the relationship between both extreme cases geometrically, approximating the sin(x) function by concatenation of intervals from real exponential, is more straightforward to understand for people who did not study complex exponential.
These two behaviors model the two extremes that the law of "offer and demand" (adding feedback from output to input of a system) can make:
- Negative feedback, with gain above 180deg phase shift: oscillation, no net gain or loss, this is equivalent to a stable feedback system on average. This is UcD amplifier technology. (I expertise in phase-shift self-oscillating audio amplification.)
- Positive feedback: exponential change in output (till something saturates or breaks in the system).
To demonstrate that my theorem proposal is not true you have to demonstrate that the difference between oscillatory or exponential responses in a system can be detected from empirical data *before* half of total investment has been gained or lost.
This does not contradict the fact that the difference between these two extreme cases can be only detected in empirical data after half of total investment has been gained or lost.
Proving the relationship between both extreme cases geometrically, approximating the sin(x) function by concatenation of intervals from real exponential, is more straightforward to understand for people who did not study complex exponential.
These two behaviors model the two extremes that the law of "offer and demand" (adding feedback from output to input of a system) can make:
- Negative feedback, with gain above 180deg phase shift: oscillation, no net gain or loss, this is equivalent to a stable feedback system on average. This is UcD amplifier technology. (I expertise in phase-shift self-oscillating audio amplification.)
- Positive feedback: exponential change in output (till something saturates or breaks in the system).
To demonstrate that my theorem proposal is not true you have to demonstrate that the difference between oscillatory or exponential responses in a system can be detected from empirical data *before* half of total investment has been gained or lost.
I'm not at that side of the wall. I live in a world governed by Control Theory. Control Theory is Control Theory everywhere. Mass is mass. Force is force. Lengh is length. Joule is Joule. Etc. The work you request has been already done by generations of researchers.
Avoiding the best moves is of course a side effect of the main feature of precognition: avoiding the worst moves.
However, all circuit or system designers:
- Shall learn by themselves to create/maintain a database discussing analytical models of the worst moves ever. This is field 1/4 of qualification. Field 2/4 is a database discussing analytical models of the best moves ever. Field 3/4 is general Mathematic/Scientific analysis methodology knowledge. Field 4/4 is application/context specific knowledge. Fields do not neccessarily have to be implemented in that order.
- Shall learn to share fields 1/4, 2/4 and 3/4 with collegues and new designers. Sharing does not neccessarily have to occur in that order.
- Shall attempt its own experiments and analysis.
- Shall, on the systems they create, learn to include structural protections against the worst moves, so that an obvious critical warning condition is issued, but minimal or no material damage has occurred at that point.
- Shall, upon their findings, consult with others for updating fields 1/4, 2/4 and 3/4.
So:
- Is "preventing the best and the worst moves" a "feature" of using precognition analysis on system output data?
- Or is using "precognition analysis" a side effect of the inability to perform "predictive structural-behavioral analysis" on system modelling data?
Avoiding the best moves is of course a side effect of the main feature of precognition: avoiding the worst moves.
However, all circuit or system designers:
- Shall learn by themselves to create/maintain a database discussing analytical models of the worst moves ever. This is field 1/4 of qualification. Field 2/4 is a database discussing analytical models of the best moves ever. Field 3/4 is general Mathematic/Scientific analysis methodology knowledge. Field 4/4 is application/context specific knowledge. Fields do not neccessarily have to be implemented in that order.
- Shall learn to share fields 1/4, 2/4 and 3/4 with collegues and new designers. Sharing does not neccessarily have to occur in that order.
- Shall attempt its own experiments and analysis.
- Shall, on the systems they create, learn to include structural protections against the worst moves, so that an obvious critical warning condition is issued, but minimal or no material damage has occurred at that point.
- Shall, upon their findings, consult with others for updating fields 1/4, 2/4 and 3/4.
So:
- Is "preventing the best and the worst moves" a "feature" of using precognition analysis on system output data?
- Or is using "precognition analysis" a side effect of the inability to perform "predictive structural-behavioral analysis" on system modelling data?
It is the normal exponential, but with a pure imaginary argument, which gives sin and cos. Give it a real argument and you get the real exponential.Eva said:
No. Not even wrong.
No. Either people understand it or they don't.
No.
No. It is the proposer of a theorem who has to prove it, which you have failed to do. Note: repetition is not a valid method of proof.
I don't know why I am bothering. Is Eva a bot?
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I wondered why you were.. Given the content of this and the other thread, it's hard to see the point...
I wondered why you were.. Given the content of this and the other thread, it's hard to see the point...
I had one of the great business economists for macroeconomics long those many decades ago, Walter Fackler. He was old enough to have known Paul Douglas who developed the Cobb-Douglas function in the 1920's. (Douglas, fwiw, enlisted in the USMC at age 50, served through many of the toughest battles of the Pacific, and was a US senator from Illinois for 3 terms - he was a revered figure by the progressive wing of the faculty, of which there werent many in the eco or biz schools.) Together Paul Douglas and Charles Cobb decided that the Euler equation would fit the bill for an accurate estimation of output given labor and capital when they collaborated in 1927.
Fackler's opinion -- Cobb-Douglas was completely inadequate.
At UChicago, they sometimes called it the Douglas-Cobb Function, similarly, depending upon who was lecturing, the nascent math behind modern option theory could be called Black-Scholes, or Scholes-Black, with the MIT portion (Robert Merton) left out in its entirety.
When the company wants to reprice options when they are hopelessly underwater that's what they use. I never was able to beat it, in fact I sucked at it. To make that clear you are offered, do nothing or take fewer shares at the current lower price the formula computes the lower number of shares.
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Eva is a very smart lady(?) and knows more about switching electronics than most who ever put foot into this forum. But you need to go back quite a few years to some old threads to appreciate.
When it come to options trading and economics in general switching electronics has little relevance.
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