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.
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✌️
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.
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.
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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?
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?
I am more fond of lingerie models...
To the point. Not used to posts like this one from you @blocktrades.
Loved it actually....and a lesson for everyone
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.
good.
I'm quoting some great philosopher here:
Garbage in, garbage out.
There are so many unknowables. And so many interested parties feeding into the equation data that will predict a favorable outcome for them.
The only principle I believe in is the uncertainty principle (and I don't even know what that is, but it sounds right).
Nobody I know (ordinary people) really trusts money, financial institutions, politicians or government. We all work hard and try to hedge our bets. Then we cross our fingers.
Also, we like to own gold, but mostly can't afford it.
Math is definitely the base of everything in this universe, now how humans are deriving the models and using them completely determines the outcome.
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.
So many things for conversation here...
On one side, we've got the need to fit into the rules of Formal Logics for our math tools to be useful. Exactly as you pointed out — sometimes information is not sufficient. But a good logician should be able to recognize the holes in the logic behind a problem. Without knowing details. It's either a case where the info covers what it claims it covers; or not. The fallacy is in the claim of sufficient information. And those are things philosophers could be right about thousands of years ago.
On the other hand, there is the usefulness of Statistics — it's a matter of scale. If it's been built on a scale where certain events can cause nothing but ripples on the surface of a larger picture, then it's reliable. If there's anything that can make a ripple as big as a tsunami wave, that will change the landscape, then we have obviously not thought on a big enough scale.
In Isaac Asimov's "Foundation saga" there exists the powerful enough mathematical model Harry Seldon calls Psychohistory (but it's still mostly maths) that predicts events in the galactic civilization for hundreds of years ahead. With all ripples smoothed out in the end.
In a system that is...wait for it...
decentralized
enough, if there's something to be done, somebody will succeed in doing it, given enough time.
That's how I understand those books.
The question is, what is a truly decentralized system? A galaxy would be relatively decentralized in my opinion. Even a portion of a galaxy could work.
We have the world to work with. And it should be enough for us since we can do nothing about the rest. Yes, we should have a good model, but we must know at all times. It is uncertain, whatever it is.
Anything set in stone lives as long as nothing too big happens to the stone.
Peace!
I remember the CDOs being explained in the movie big short by Selena Gomez. I loved that they did that so us normies can try and understand. I knew nothing about them at the time.
Youre right. Complicated enough to look legitimate but they dont take everything in account, like many things in finance. :)
I still need to leave my answer even though, lol.
Since the ice container was not mentioned. I therefore specify nil/zero because Bob took 2 in the morning when it was still frosty.
So definitely afternoon there will be change in temperature.
But I love the life lessons behind the question.
Congratulations @blocktrades!
Your post was mentioned in the Steem Hit Parade in the following category:
Hi. Obviously, since the question is read, it is perceived that there is a trap.
Mathematical models are fabulous but largely based on ideal situations.
All human beings are absolutely different. We may have similar reactions to certain stimuli but that cannot predict human behavior.
Very interesting observation and the warning you make in this post. Regards @blocktrades
@blocktrades Hey Blocktrades, I see that you have sponsored a couple sports contests in the past and I was wondering if you would be interested in sponsoring mine? I have been running it for 2 years now and I think with some more exposure it could help attract some more people and help keep them here. It's a good way for a getting a bit more fun on here, which I think we all would like to see some more of. I could even set up a banner at the bottom that directs users to your crypto exchange or something. Hit me up here or on steemchat if you would like to chat a bit more about it. Thanks in advance!
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That was at last an interesting read! Thanks!
I've never been one to trust mathematical or statistical data when it comes to critical aspects of my life like investing my money. I rather do my very little research, see the numbers that I guess we could say is mathematics but ultimately, I follow my gut and then make contingency plan in the vent of an unexpected outcome.