It's brilliant, and it will work, and continue to work until people don't believe in it.
Do you not understand how gambling works?
Social security, now that I think about it, does sound much like a Ponzi scheme.
No it isn't. If everyone has one or less children, the population does not grow exponentially.
That's not trolling. It's called "mathematics."
The OP's comment, including " ... changing the common definition of exponential by saying the exponent could be 1 or less than one" is (a) mathematical and (b) wrong and misleading. The "common definition of exponential" accommodates any valid argument to exp(x), and to claim otherwise requires a mathematical correction to avoid misleading people.
That said, I was not intentionally trolling. I do think it's possible for a SS-style benefit to sustain itself provided that an exponentially growing population, whose exponent is greater than 1, is obligated to pay in.
A country with a stagnant or declining population will probably have trouble.
You may disagree, that's fine.
Nevertheless, any population whose growth (or lack of growth) is defined by the average number of children per member will behave exponentially.
Behave exponentially != grow exponentially, still utterly missing the point; still trolling.
False. An exponential function, and a growing exponential function, differ only in the value of the exponent.
Here's an equation that predicts future population based on the value of an exponential term:
The equation: pt - p0 e^rt
pt = population at time t
p0 = present population
r = rate of population growth, 1% = .01
t = time
A result at 40 years for a population rate of change of -1.7% per year:
e^(-.017 * 40) = .5066
This result says that, for a population growth rate of -1.7%, after 40 years the population will be about half its present size. It's an exponential result, it's even an exponential growth rate, but the growth rate is negative.
In this image:
http://i.imgur.com/LW6bk8t.png
The red trace is an exponential rate of change for r = +1.7%, the green trace for r = -1.7%. Both are exponential results, and both reflect what a population would look like for given r values.
We're not talking about how to model population growth, or functions, we're talking about whether every couple having one child results in exponential growth and it simply does not. If the population decreases, that is not exponential growth. An exponential result != exponential growth. You are wrong and we are done.
You need to learn mathematics (as well as grammar). Also learn "negative growth rate" while you're about it:
http://wiki.answers.com/Q/Is_it_possible_to_have_a_negative_...
And, everything else aside, all the described rates are exponential.
> We're not talking about how to model population growth ...
WHAT?? Here is what you said: "If everyone has one or less children, the population does not grow exponentially." How exactly is that NOT talking about how to model population growth?
Also, it's "one or fewer children," not "one or less children."
> An exponential result != exponential growth
False in a discussion about population and exponential growth rates, terms you chose.
I posted the proof of my position, you posted your ignorant opinion.
Here is another reference that makes the same point in the same way:
Source: http://en.wikipedia.org/wiki/Exponential_growth
Quotation: "The formula for exponential growth of a variable x at the (positive or negative) growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is xt = x0 (1 + r)^t"
Let me emphasize that for you, in case your eyes are giving out:
"THE FORMULA FOR EXPONENTIAL GROWTH OF A VARIABLE X AT THE (POSITIVE OR NEGATIVE) GROWTH RATE R ..."
Now circle the word you're most unfamiliar with, raise your hand, and the teacher will administer a sedative.
You've been told numerous times to stop thinking about math and read the words but you clearly don't grok or can't remove your math head and have normal conversation. You're still talking about modelling growth, no one else is or was. Turn off your math head and read the English words using their lay definitions, a decline in population is not exponential growth as a decline in population is not any kind of growth because it isn't growth. If you can't bring yourself to admit that, you are beyond hope.
Secondly, I'm a computer programmer, I understand the math, so stop trying to lecture me on math when you're the one not listening. I can't help it you don't understand the point being made to you because you lack the ability to be aware of the context of the conversation you're in. I know what I'm trying to communicate and I've made it as clear as I can numerous ways; if your brain is unable to work in multiple contexts, that's your failing in understanding how to communicate with others.
If you try and prove your point with equations one more time, or reference them one more time, then you've utterly failed to understand what is being communicated to you and we're done because I don't talk to brick walls who can't think.
Did you know that Social Security taxes were once 2.25% of income? Before they were 4.5%? Before they were 6.9%? Before they were 8.1%? Before they were 15.3%? That's where we are in 2014.
To be fair, while Social Security is clearly not an annuity, as of 2014 it isn't yet in default of its obligations. There's some dispute about what year that will inevitably happen. It will not be described as a default when it does, but rather tweaking a few formulas to protect America's most vulnerable citizens.
Edit: Social Security also has some "constructive default" options which are available outside of the program, because it is coextensive with the taxing power of the federal government. For example, SS benefits were once untaxed but are now taxed. There exist plausible ways by which every dollar promised of SS benefits can be "paid" but in which many get immediately recaptured by the government, which avoids formally adjusting the terms of the promise but which is indistinguishable from default in its impact on e.g. your family's budgeting process in 2070.
Another option is inflating away the insolvency. Japan will probably do this. It will pay out every yen of the promised monthly 200,000 yen due to pensioners, but pay it with yen which buy half as many apples as they did back when the pensioners were working.
You have a standard lie in your screed above, which when revealed demonstrates exactly how the zero-sum game will shift during our lifetimes to keep Social Security solvent forever and ever, amen. You claim that Social Security has no investments. This is a blatant lie. Social Security has been running a surplus for all of my life, and investing the surplus in trillions and trillions of US government debt, partially because it's the safest investment in the world and probably mostly because it's really convenient for the government.
Ah-ha, I'm sure you're going to say. When the one hand cashes in the T-bills, the other hand will have to pick our pockets to pay for it with more taxation, you're going to say.
Yes. But which pockets the government picks to pay off our internal obligations is extremely important.
Social Security, you see, is funded by a more-or-less flat tax on the first $XYZ,000 of workers incomes. It is basically the most regressive a tax can be, short of it being a fixed dollar amount regardless of income, which usually only happens for licensing fees, but that's another story. On the other hand, the mature T-bills are going to be paid for out of the general fund, the taxation structure for which is honestly one of the more progressive tax bases in the world.
When you combine this with the most probable fixes for Social Security -- dropping the income cap on the tax -- the future of Social Security is quite clear. Social Security is going to quietly shift from intergenerational wealth transfers to intragenerational wealth transfers. Some people in a generation, the poorest, will get back more money from Social Security than they pay in. Some people in a generation, the richest, will pay in more money than they get back.
The difference between Social Security and a Ponzi scheme is that, in a Ponzi scheme, if every group did not statistically get back more than they paid in, they would stop paying into it. Social Security, being involuntary, can collect 15% of $250,000 from a man while telling him upfront and outright he's only getting back 15% of $150,000 after he retires. At this point, a Ponzi scheme would collapse. Social Security will just putter along happily, running exactly as it should.
The difference between a Ponzi scheme and Social Security is that a Ponzi scheme is an investment, while Social Security is an insurance. As an insurance, a statistical loss is expected, but it provides a guarantee, in this case that when you are old you will never be destitute, living on the street eating catfood, or cats and rats when you can catch them.
Think harder, it's nothing like a Ponzi scheme, it's just like any other insurance; payout is not guaranteed.
I suppose they are similar in that neither are actual investment vehicles, despite what many contributors tend to think.