Alice has 5 ice cubes, Bob takes 3, how many ice cubes does Alice have left for her afternoon Thai iced tea?
If you’re good at solving word problems from elementary math, you’ve probably answered “2” (or even if you weren’t great at word problems, since this is a particularly simple example of such a problem).
If you’re an “out-of-the-box” thinker, you might have said “not sure, but maybe zero” since I didn’t specify where the ice cubes were stored, what the temperature was (did the reference to Thai iced tea mean there’s a high probability that Alice is in relatively hot Thailand?), or how long before Alice takes her afternoon tea.
Why are you asking us silly math questions?
Strictly speaking, the title question isn’t really a math problem. For example, if you had talked to Alice this evening, she might have told you that the weather was so hot that all her ice melted before she could put it in her afternoon tea.
The question only becomes a mathematically solvable problem if we’re able to capture all the relevant information needed in a way that we can represent with math. You may even feel like I was “cheating” when I asked the question, since it sounded like I was asking a question where I was implicitly promising that all the relevant information was there, so all you needed to do was apply your knowledge of math to solve the problem.
Mathematical reasoning is an incredibly powerful tool and has led us to advances in many areas of science. But because it has solved so many problems, it is easy to be persuaded by arguments that use mathematical arguments. After all, you can work through the math and see that all the math is correct.
But what I was trying to point out with my original question is that it’s very easy when constructing a mathematical model to miss elements of the real problem you’re trying to analyze, resulting in a model that is persuasive because of its mathematical correctness, but is completely wrong as a predictive model of the real world.
The more complex the system you’re trying to model with math, the more likely you are to miss important elements that destroy the predictive power of the model. Mathematical models that attempt to predict human behavior are particularly prone to flaws because of the many factors that influence human behavior, making it difficult to capture all these factors in the model. Despite this weakness, there are endless attempts to use math to model human behavior, because there’s a lot of money to be made from correctly predicting future human behavior (stocks, politics, etc).
Ok, sure, but does this result in real world problems?
The real estate bubble and resulting financial crisis of 2007-2008 had their origins in a mathematical model that improperly predicted the “safety” of financial derivatives known as collateralized debt obligations (CDOs for short).
The CDO model was just complicated enough to look reasonable, but still failed to adequately model human behavior. Among other things, it failed to model the fact that the use of this formula itself as a means of valuing CDOs would encourage a loosening in standards for home lending rules that ultimately increased the amount of home owners who could not or would not maintain payments on their home loans when they encountered financial distress.
Ok, so should we just distrust all math models?!?
No, math models are great tools and have lots of uses. But the next time you see someone predicting human behavior based on a math model, I suggest the best place to look for flaws isn’t in the math itself. Look for things the model may miss.
And be very skeptical about the ability of that model to capture all the things that go into a human’s decision making process.
That was at last an interesting read! Thanks!
I am enjoying the topic.
The more data you have, the more aspects of the world you can consider. Someone creating a mathematical model may consider 10 or 20 variables. They may have solid, written data about the historical values of those variables. In the best-case scenario, they may be quite sure that they have good, reliable data. But still, it's just 10-20 variables. What are the consequences of not considering all sorts of other variables that may have big impacts?
Someone just pondering over the problem for a little bit may consider thousands of variables based on their experience (their nervous system having recorded actions and their consequences as they propagate through the system). But that data is not reliably stored - our nervous systems change our memories over time, the memories may get recorded in problematic ways to begin with, and so on.
Maybe we can take the best of both worlds - reliability of data AND system-wide mapping. There are various models that endeavor to do this.
This is really deep. I had so many answers from word problem answers to logical answers😄. I agree with your point on the fact that maths can be used to correctly predict future human behaviours. It's endless what can be done with mathematics. Thanks for sharing✌️
Bob have X steempower, 10 upvotes and 2.5 downvotes. On top of that we have xy reward curve. Add a couple of bots and curation trails. Then we have a couple of smart guys who suggest HF.
Not to mention the bear market and a bunch of greedy people.
Guess where we're heading?
Nicolas NAssib Taleb already said in his book The black swan, the impact of the highly unlikely, that most of the decisions made revolve around the Gaussian curve or bell curve without considering the entire surrounding environment of the queues , that in the end when something fails and it is something very unlikely, it is never considered that it will generate so much damage, and it is what happens as a great earthquake or what you say the subprime crisis of 2008 that caused so much damage.But well, there is no model capable of efficiently predicting what we should do is take what is there and take the logic that it could go wrong, as if and if they cut all the internet connections that will happen with the blockchain and the crypto world, I I have asked, it is not something crazy can happen, a couple of cables, satellites and goodbye cryptos, but hey we must think about that.Thank you for making us think of pretty laughable things like these.
Everyone else did not think “unsure” as I didn’t know enough about the current state of the ice cubes?
Googles crazy algorithm should be enough to show there are just some things about humans that have yet to be squeezed into a model. That won’t stop them from getting close.
As far as the next economic collapse far too many seem to be running around saying “since everyone is talking about it we are safe.” Which makes me think oh duck are they about to be proven wrong again?
The non-mathematical answer, or at least one of them is Alice still has 5 ice cubes, because she was out on a date with Bob, and when he ordered his drink he wanted to show Alice how much of a man he was and asked to have the bartender only put in 3 ice cubes in his drink.
When looking for solutions, the more clear the question, the more clear the answer. I agree, I do not think any math model can capture all the things that go into a human decision. People just do not think the same as the person that is sitting right next to them, they do not see the same things the person sitting right next to them see either.
Great stuff! So glad to see someone else having the same kind of thinking! Most people are too dependent on models and too attached to dogma and ‘ceteris paribus’ everything being equal!
I could never trust in Pareto Optimum either!
Cheers.
5 - presuming bob took the 3 ice cubes to make her iced tea.