[playeren]

I made this mistake once, albeit with Newtons second law instead. I was explaining my estimations for changing some key processes in a company. As a kind of mental aid, I used 'F' as the total effort needed to make the change, while 'm' represented the size of the organization, and 'a' would represent the speed we wanted to perform the change with. F = m * a. A simple way of illustrating the exponential relationship between these factors.

But it blew their mind. It took on 'mystical' properties, as if we had distilled change management into pure Newtonian motion. I started seeing not only F = ma in memos on other issues, but also other equations like E = mc^2, trying to wrestle management lingo into relativistic conservation of energy.

Lesson learned, I guess.

[cycomanic]

> I used 'F' as the total effort needed to make the change, while 'm' represented the size of the organization, and 'a' would represent the speed we wanted to perform the change with. F = m * a. A simple way of illustrating the exponential relationship between these factors.

Am I missing a certain insight or did you mean the linear relationship not exponential?

[wolfram74]

No one uses expontential correctly in colloquial contexts, it gets slapped on any super linear curve, or in this case even a linear equation.

[the_af]

But using exponential to mean a linear equation is all sorts of wrong, even in a colloquial sense.

I would understand a colloquial meaning of "exponential" as "it grows faster than linear". Wrong, but it makes informal sense. But using is as a synonym for linear makes no sense whatsoever.

[colechristensen]

What is your definition of exponential then?

[glass_of_water]

A function f(x) whose growth rate at x is proportional to f(x). So anything where growth rate is proportional to the current value.

[crdrost]

There were a bunch of answers, but this is the one that is the most handy in my toolkit.

Linear growth of A on B: For every new B, k new As emerge, for some k (could be and often is fractional).

Quadratic growth of A on B: A grows approximately linearly with the number of handshakes in B, so that in the above language, for every new B, k × B new As emerge, one k for every existing B that the new B could interact with.

On this basis one would say that the number of bugs is quadratic in the lines of source code. Each line has some small probability of interacting with some distant line in some non-negligible buggy way.

Exponential growth of A on B: A grows approximately linearly with the number of connections between A and B, so that in the above language, for every new B, k × A new As emerge, one k for every A that the new B could interact with.

So for “knowledge increases exponentially,” the precise technical claim is that it increases exponentially with time, and this means (somewhat dubiously for long scales) that in a given period of time, every every fact you know has a constant probability of generating a new fact which you now also know. This holds when you don't know very much about a new scenario but tends to be tempered out rapidly, the phenomenon of “low hanging fruit” etc. A meme similarly has an approximately exponential region where the number of folks exposed to the meme drives further exposure to the meme, but this dries up as the probability of “already shared it!” rises and curtails that “I must share it with friends” impulse.

[no_identd]

>"knowledge increases exponentially"

Personally I suspect that as (slightly) false and that it's actually something like quadratic-hyperbolic growth, which looks awfully similar to exponential growth if you don't zoom in.

[marginalia_nu]

f(x) = 0 is the rarest exponential function of them all.

[crdrost]

It grows in every way, because it grows in no way. Does a dog have the Buddha nature?

[fsckboy]

humans learn words through contextual exposure to them.

exponential has two meanings depending whether you studied and understood what exponentials are in a math class, or did not.

if you did not but you've learned the word through repeated verbal contexts, it means "bigly"

also, in the example given of F=ma, the "a" is characterized as "speed" (per second) which it is not; but rather "acceleration" (per second per second) which is related to speed via an integration over time (seconds), but that's a f(unctional) relationship as is exponentiation, so from context I think people pick up that exponential means something like biglyly

(When I read the Mysticization title I was prepared for a pun on the game Myst, but it didn't show up. Myst and SimCity date from the same period of time, and SimCity is a system dynamics game. I was disappoint.)

[rzzzt]

Exponential: f(x) ~ n^x ("n" is constant, "x" is the exponent)

Parabola: f(x) ~ x^m ("x" is the base, "m" is constant)

[igorkraw]

Your variable goes into exponent position. If X is your variable, a^x is exponential, x^a is a-tic

[kittiepryde]

y=x^a would be an example of an exponential equation;

I guess applied to the metaphor, F=a^m

[orbital223]

f(x) = x^a is a polynomial of degree a.

f(x) = a^x would be an exponential function.

[kittiepryde]

You are right. Thanks for correcting me.

[bsilvereagle]

I suspect F was fixed and the curves were showing how m/a varied in that case, in a similar fashion to these plots for momentum: https://frdmtoplay.com/on-a-researchers-momentum/

[mjburgess]

I hope one day to possess an explanation of why that behaviour is sometimes good. Since, like you, I am alarmed/concerned by it. But clearly, largely, its what makes "a lot of the world go round".

This emotion, "wonder", is profoundly suspicious to me; and I'm often hostile to it. I am sure I'm missing something...

[roenxi]

People are trying to copy the smartest person in the room, but don't themselves have a good way of evaluating how smart an idea is. When that strategy produces a miss, it produces a rather absurd one (like in this anecdote).

But the strategy itself is good, particularly if the group correctly identifies who has the best ideas. Copying smart people works if you can find them.

[marcosdumay]

> Copying smart people works if you can find them.

Well, works more often than not (I hope your downside risks are low). While understanding what they are doing works almost every time.

Besides, it works more often than not, in a simple setting where there is no antagonistic communicator. In a word with propaganda and politics, it fails almost every time.

[a1369209993]

> understanding what they are doing works almost every time.

To be fair, understanding what they are doing requires being smart yourself (usualy not as smart as coming up with it in the first place, but only usually), and while smartness isn't always or completely unlearnable, in practice it's usually hard and/or impractical, especially if you're not smart to begin with.

Of course, distinguishing (honest) smart people from (possibly smart) con artists also generally requires being smart, so that doesn't help much.

[ouid]

>The strategy itself is good.

You cannot factor the strategy from its implementation here. I think that was trying to be your point but then you contradicted yourself. I must encourage you to commit. A dumb person who tries to find smart people will find only con-artists. Its the law of lemons.

[roenxi]

A strategy doesn't have to work every time to be good. "Dumb people" can and do find people smarter than themselves and put in an effort to copy them. Usually that is a good idea - better than trying to go it alone, any way.

[ouid]

My brother in christ, most of the people who voted for donald trump did so because they think he's smart. Its a good goal. its a terrible strategy.

[roenxi]

That is a slightly different situation though, isn't it? The US presidential elections are a choice between 2 options, usually both bad. The results suggest all 3 candidates in the last 2 US elections are borderline unelectable and both parties are engaged in a bizarre war to find the worst candidate people will vote for.

Which is not at all the same as the fairly typical group dynamics.

[philipov]

Wonder is what drives people to be interested in and want to learn about how the world works. It's a very important emotion to let thrive. But, like all good things, too much of it can become harmful. Wonder is best when tempered with rigor. It is a starting point, but it must not also be the ending point.

[noSyncCloud]

If you can't experience wonder, that must make you history's most recent example of someone who's basically figured everything out. That must be very nice for you, but you are assuredly wrong about many things that you know you know.

[delusional]

It could also be depression or just cynicism.

[drewcoo]

So you claimed "total effort equal orgs size times the speed you wanted change in?" And that that was equivalent to F = m * a?

That's not mind-blowing so much as jaw-droppingly wrong. Org size is an exponential factor for things like that. And speed of change isn't the issue for orgs so much as changing direction under the current momentum, if we're using a physical model. No wonder it wasn't met with widespread acceptance.

It was a vast oversimplification that mapped badly to the situation but delivered, no doubt, with confidence, so of course it was adopted by copycats. Simplicity and overconfidence sells.

[lukifer]

Accuracy, utility, elegance: pick two.

[bmacho]

Pick any two and the third comes for free