There are mathematical certainties. In this instance we have that all exponentially growing bubbles will necessarily display the property that values grow and at an increasing rate just before the bubble bursts. This is so fundamental that I can't believe you don't see it. You can construct the growth curve out of this very fact alone. Therefore, the simple fact of growing values and increasing rates of growth in values is not determining bubble/non-bubble.

In other words, the statement "I know I am not chasing a bubble because valuations are high and growing at an increasing rate" is categorically false because this property is a common indicator of the exact opposite; that you are in an exponentially growing bubble.

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kbrkbr 6 days ago | parent | next [-]

Look, neither did I say there are no mathematical certainties, nor did I anywhere argue about the content of what you said.

The only thing I said is: there are probably no _obvious_ mathematical certainties in reply to what you said, as the history of mathematics shows with plenty of examples.

But it's already too much ink spilled for such a little difference.

I reckon now that you use words like "obvious" (or "categorically" in the last reply [1]) as markers of belief strength or something. That's fine, many people do it.

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d4rkn0d3z 6 days ago | parent [-]

> "Look, neither did I say there are no mathematical certainties, nor did I anywhere argue about the content of what you said

The only thing I said is: there are probably no _obvious_ mathematical certainties in reply to what you said, as the history of mathematics shows with plenty of examples."

There is nothing more obvious and certain mathematically than the fact that exponential growth of bubbles entails increasing valuations and increasing rates of growth in those valuations.

I use the word "obvious" quite properly as in "can be read from any graph", or "is contained within the structure or the model". I use categorical because the implied conclusion of the original comment is a categorical error.

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kbrkbr 6 days ago | parent [-]

There are people who disagree. Here is one compilation of theorems that are obvious and false:

https://math.stackexchange.com/questions/820686/obvious-theo...

	▲	d4rkn0d3z 6 days ago \| parent [-]
		This is not a theorem, it is a property of the model.

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kbrkbr 6 days ago | parent | prev [-]

But I think I should be giving a reply also to the content of what you say. That's only fair after you took so much time explaining.

I think you conflate two questions in your statement: the question of what can be said about a function that is up to a point exponential and growing, and after that point decaying in an unspecified manner, but so that this point is a local maximum. And secondly the question if this is a good/the only/the best model for valuations in what is called an investment bubble that then bursts.

This conflation of model and modeled makes it hard for me to assess the argument, because I need to take these layers apart, and that involves guess work.

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d4rkn0d3z 6 days ago | parent [-]

There are no layers and I am trying to help you in your difficulty. It is not sound to look around and observe increasing valuations, or increases in the rate of growth of valuations and thereby conclude you are not observing a bubble. It is actually more sound to say that what you are observing is consistent with our model of bubble dynamics.

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kbrkbr 6 days ago | parent [-]

Here is an example of the mix-up (from a bit above):

> The greatest values, and change in values comes just before the bubble bursts.

This seems to be talking about the mathematical model. Then you go on:

> In fact, tulips were most valuable, and those values were climbing at the highest rate before the tulip bubble burst.

That seems a jump to the modeled. And you speak of the modeled as if it was the model.

And by the way, if this graph [1] is correct, then what you say is also false. The valuations do not rise exponentially, but slow before the bubble bursts, very visibly. This is also true for the 2008 housing bubble in the local index [2].

I think that shows quite well that there are two layers. And there is the question of the fit between them. Having seen those two graphs I think I'd rather expect reduction in the rate of change of valuation shortly before the bubble bursts. That model appears to fit better what I'd expect in economical bubbles (but not in soap bubbles), namely a growing sense of risk that counteracts the fomo.

[1] image Tulip Price Index 1636-37 here https://www.historydefined.net/how-did-tulips-create-the-wor... [2] https://wolfstreet.com/wp-content/uploads/2021/07/US-Housing...

	▲	d4rkn0d3z 6 days ago \| parent [-]
		There is no issue with stating the model and an example of the modeled in the real world such as tulips. You are simply taking a favourable view on when the bubble "burst" occurs in order to see what you want. My point stands that valuations and there growth are not really distinguishing bubble/non-bubble. Thanks for proving me correct in that.