honestly, the very title speaks to the problem. Mathematics is based on boolean logic, if it aint right, it's wrong. Then they start with assumptions and start trying to see what conclusions can be had with the requirement that all such conclusions be self-consistent (meaning, no conclusion can disagree with another conclusion, ever). Which is really useful, but the issue is that the real world isn't always that black and white. To be successful is often about being 'less wrong' than the other guy, but less wrong isn't something that mathematics understands. There are systems put in place to try and quantify such things, in particular bayesian probability and multi-valued logic systems ('fuzzy logic' is one such example). And they're extremely useful, fuzzy logic in particular is really fun to think about imo, but at the end of the day, mathematics is a philosophy with a requirement to be self-consistent, not to be in any way useful or applicable to the world as we know it (PI cannot exist in our physical reality, only an approximation of it, for example). I haven't read the book, so I cannot really talk to the contents, but I take issue with the idea represented by the title. It isn't about mathematical thinking, and it sure as hell isn't about 'not being wrong'. In the real world, it's about being effective, and that means being better than the other guy. Mathematics in general is about perfection and purity.
You do have a point there, but don't you think Maths as a tool can be used to be "less wrong"? I haven't read the book either so I am not sure if the author is trying to talk in absolutes but in real life application, Mathematical tools such as Statistical Analysis are used only to be less wrong i.e. nobody in their right mind believes that the results would be accurately predicted by Statistical analysis but they are useful to make better guesses. PS: Not an Academic but I do use Statistics for Financial Analysis in my work. Edit: Grammar
Math is a tool that can be used, as in your example of financial analysis. In general Steve Jobs made great decisions but I suspect he didn't rely on Mathematical Reasoning to do so. He certainly used statistics and the like to help him make decisions, but this is a far cry from what the title of that book is implying. There is a difference between relying on things such as statistics to help guide your decisions, and using "mathematical thinking".
Hmm... I may be taking the discussion to a different direction but I was wondering, is there a way to know that a decision that was taken was the "most right" decision? For e.g., you mentioned Steve Jobs making great decision. Even with hindsight what if there were better decision that he could have taken and how can we know if such a decision or a path even exist? Sorry if I am not being clear. Let me try to illustrate with an example: Let us say you make a decision A which resulted in an outcome where you made $10 of economical profit. You think that this decision was a great decision as overall you were profitable. Until and unless another person shows you a decision B which would result in a profit of more than $10 you can never know if your decision was the "most right" decision. I guess what I am trying to say here is that unless you include a measure of objectivity there is no way to know what is the "Most right" choice at all. Intuition and subjective insights are great but you can never be sure if they were the best solution unless there is some objective way of proving that all the other decisions would have resulted in an inferior result.
First place only has to be better than Second place in order to be First Place. Sound Obvious? First Place doesn't need to know that they have the absolute fastest possible 100 meter dash, they only need a 100 meter dash that is faster than everyone else. That's why I said the following:In the real world, it's about being effective, and that means being better than the other guy.
But if you are not sure that you have the absolute fastest possible 100 meter dash then there is always a possibility that someone else will figure out the way to get it and your win is just temporary achievement. What used to be the record for 100 m dash at one point of time can't ensure even a third place in the modern sport. Your thoughts on this?First Place doesn't need to know that they have the absolute fastest possible 100 meter dash, they only need a 100 meter dash that is faster than everyone else.
First place is first place. Do you think someone like Bill Gates is going to question whether or not his decisions were the right ones because someone in 2314 might be worth more money than he is now? We can stretch this out to ridiculous proportions, but it won't change my initial point. You can talk about local vs global maxima all day long, that sort of stuff only really matters to a mathematician. In the real world, we judge our achievements in relation to those around us, not to idealized perfection. Is Gordon Ramsay a great chef because he's perfect and no one can ever be as good, or better than him, or is he a great chef because he's arguably better than everyone else?