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337 comments on DrumBeat: November 8, 2008

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Pitt the Elder on November 8, 2008 - 4:08pm Permalink | Subthread | Parent | Comments top

Debt = e(No of years * ln(1 + interest %))

eix = cos(x) + isin(x)

It's highly misleading to suggest that these two equations are similar; their behaviour is completely and utterly different. Writing a complex number as (x,y), the equations become:

  1. e^x = e^(x,0)
  2. e^ix = e^(0,x)

The first equation is the regular exponential function we're all familiar with, and quickly produces very large numbers; the second equation describes the circle of radius 1 centred at the origin. The results are not even remotely similar.

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elwoodelmore on November 8, 2008 - 6:42pm Permalink | Subthread | Parent | Comments top

as long as we are picking nits, i believe the first equation should read:

d=p*(1+i)^t

where p is the principal , i is annual interest rate,fraction(not as %)
and t is time,yrs

example i = 0.05 t=5 then debt is p(1.05)^5
= 1.28p

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WebHubbleTelescope on November 8, 2008 - 10:58pm Permalink | Subthread | Parent | Comments top

If they do something like
d2Debt/dt2 = K - c*Debt
which shows Debt accelerating until it crosses some artificial limit, it will start oscillating, as the solution to this equation is a phased sin/cos equation.

Why this would happen, I don't know, but it is mathematically one way it would start oscillating.

I would think the debt would crash or reset before oscillating.

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Don in Maine on November 9, 2008 - 3:15am Permalink | Subthread | Parent | Comments top

I would think that oscillating is actually the norm, and we will see much more of that before we see a crash or reset.

Don in Maine

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WebHubbleTelescope on November 9, 2008 - 10:49am Permalink | Subthread | Parent | Comments top

The yearly deficit seems to oscillate a bit but the accumulated debt keeps on increasing.

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Paleocon on November 9, 2008 - 11:09am Permalink | Subthread | Parent | Comments top

Would not an oscillation in debt require a feedback loop and a gain of greater than one, as in classical control theory?

I know there are other theoretical modes that can drive oscillatory behavior, but I can't see what would drive a debt oscillation other than such a feedback loop consisting of changes in interest rate, regulation, and behavior. Likely any such oscillation would be on a very long scale -- to the tune of decades. Perhaps there is short-duration cycle overlaid upon a much larger generational cycle?

I am sure that there have been attempts to model economic theory in terms of overdamped and underdamped systems, with various input functions and signal paths, but the complexity would likely be intractable. A discrete simulation with enough interconnected but independently acting entities might be viable.

I imagine that social mores and emotional readings like "consumer confidence" play into any such mechanism, but maybe those could be quantified in some way as well.

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css1971 on November 9, 2008 - 5:33pm Permalink | Subthread | Parent | Comments top

Likely any such oscillation would be on a very long scale -- to the tune of decades.

You mean something like this:
http://www.thepiggybanker.com/wp-content/uploads/2007/04/interest_rate_c...

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DIYer on November 9, 2008 - 11:44am Permalink | Subthread | Parent | Comments top

I think we had discussed, or at least mentioned, the L-V equation a while back, and I think it applies. Depending on the parameters, it can assume a nearly constant steady state, oscillate (almost- but not-quite- sinusoidally), oscillate wildly, or crash.

Just substitute fossil fuel for "prey" and the financial system for "predator".

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css1971 on November 9, 2008 - 4:59pm Permalink | Subthread | Parent | Comments top

I wasn't really suggesting they're similar I was just pointing out that exponentials are closely related to functions which form waves and are therefore likely to vary wildly.

When trying to measure the size, or value of an item, it really doesn't seem wise to use something which is itself likely to vary wildly. In fact, the very idea is ridiculous. Would you use an elastic band to measure the width of a door?

How can credit then be said to be a good way of measuring the value of something? How could anyone possibly reliably gauge the value of anything when the value of money itself is based on millions of loan agreements and debt payments.

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337 comments on DrumBeat: November 8, 2008

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