Good content, but my favorite part of the article is the anecdote about how Paul started at Google. Putting yourself in a place where you have the opportunity to be lucky makes up some percentage of the total likelihood of being extremely successful (yes, I consider Paul extremely successful along many axes), but I think a much larger portion of this equation is actually being lucky. I guess if you iterate over and over again, by say joining startups repeatedly, eventually most people get lucky in some way. The magnitude of that success however, is certainly highly variant.
If you tie your success to only how well a company is going to do, you are setting up for fail (And feeling unlucky, and so slightly pissed off at work.). There are too many external factors deciding that.
I measure my success in many ways.
1. Do I havea loving family. Check.
2. Do I have fulfilling hobbies. Check.
3. Do I have enough money to fulfill my responsibilities and hobby, doing things I love. Check.
4. Do I have as much money as I would want to call myself successful. Not yet.
Tying my success to many parameters I can feel a little successful everyday, and continue to feel lucky, and continue to work toward what I would call a successful startup.
This reminds me of portfolio theory in finance: as long as your goals are diverse enough, generally you will track the market (i.e. how life is going generally). That being said, I think the most successful business people are those that really closely tie their happiness with the success of the company (Steve Jobs, I think, is a good example).
If you feel he's a good role model, then what do we make of him being cast out of Eden by his own board, and then having NeXT going basically nowhere until Apple begged him to come back and bought the company for its OS and as a talent acquisition?
I suspect he's been happier in a certain sense when his actions have been validated by the market, but at the same time, I strongly suspect he has certain other motivations that drive him and he's happy when he acts in harmony with those motivations. The marketplace validating his work is probably just icing on the cake.
That's all just speculation I pulled out of my Ass, of course!
This is even stronger than Pasteur's famous, "Chance favors the prepared mind" - if you are not actually working on a problem, there is no possible way to benefit from serendipity.
The article mentions a few fairly vague examples of what this type of algorithm is used for. To all of you non-neophytes, what are some specific implementations of this algorithm and where are they used?
If you write the equations describing the flows in a mass-conserving system, you can end up with a symmetric diagonally-dominant system.
As you might expect, there's a physical interpretation.
Diagonal dominance basically means that the diagonal entry of each row of the matrix is at least as big (in magnitude) as the sum of the off-diagonal entries.
Suppose the diagonal entry gives the rate of change of flow (say of a fluid, or of electric charge) into some physical location as you change some other property of that location (like its pressure, or voltage). Then the off-diagonals in the same column reflect the rates of change of flows to other locations as you change its pressure. And the off-diagonals on the same row reflect the rates of change of flows out of that location as you change the pressures in other locations.
If the flows are driven by pressure or voltage differences-- which is often the case, especially when you've linearized the system mathematically-- you get symmetry (because adding 1 volt to node A has the same effect on the A-to-B flow as subtracting 1 volt from node B).
If the system conserves mass (or electric charge or whatever), then the diagonals must at least add up to off-diagonals (in magnitude).
So then all you need is a connection to an outside node of known pressure or voltage (like ground), that doesn't change and hence doesn't contribute to the off-diagonals. That kicks one node over into having a diagonal entry greater than its off-diagonals, and then you have a nonsingular matrix and you can apply the algorithm.
Disclaimer-- it's been a while since I worked on this, so I probably messed up at least one of the directions or row-wise vs. column-wise relationships.
Let's say you're manufacturing a product with thousands of individual components, each of which has a different cost, a different lead time, a different shelf life, and so on. These thousands of components are made into hundreds of sub assemblies, then tens, then are finally assembled and you have your product. You can crunch all of that and answer questions such as, in what order should we do this? How much of each component should we keep in stock? How does the rate at which we work affect the final cost? Would it actually be cheaper per unit to open another assembly line? And so on.
Please elaborate. Solving linear equations with software is nothing new, this algorithm just does it faster. So I'd like to see prior art for what you're describing here, sounds interesting. How exactly would one apply linear algebra to solving the first and third questions for example?
Back in college a few years ago, we mostly used Simplex and other tableau-pivot based algorithms for solving large linear programming problems. Link to wikipedia article on the Simplex algorithm http://en.wikipedia.org/wiki/Simplex_algorithm
For most problems that individuals face each day, linear programs are fairly simple to model and solve. However, there are lots of complex problems that are solved each day.
A few examples of large-scale linear programming problems:
- For Amazon.com: what quantity of each item should be stocked at each warehouse each day to minimize inventory while also optimizing for shipping time and cost to demand nodes (customers).
- For an airline: how to plan and schedule flights to all domestic and international airports to maximize profit
- In shipping logistics: how to allocate trucks and set routes to minimize fuel cost while satisfying delivery time.
For complex systems, you can easily run up a linear program with millions of independent variables (producing millions of rows in the linear system).
Solving a linear system of equations is not the same as solving a linear program. The article is about the former, not the latter. Linear programming is an optimization problem, subject to constraints that are described by inequalities. Linear systems of equations are finding values of relationships defined by equalities. There are lots of matrix multiplications involved in both, but other than that the solutions don't really resemble each other. For example, Linear Programming is not even known to be solvable in strongly polynomial time (simplex is exponential in the worst case, and the best method is weakly polynomial), while the algorithm in the paper improves from one strongly polynomial result ot another.
Doesn't that 5,057 include "other professional degrees"? Further, are these only from accredited schools? Both could greatly reduce the effect of this particular statistic. That said, it is always disheartening to be reminded of the poor folks who likely shelled out tons of money only to find there were no jobs on the other end.
I think he may just be suggesting forming as an LLC or some other entity that both shields you from liability, and doesn't dissolve when one partner calls it quits.
I think they are also trying to help consumers. I listened to an interview where they said they have people on staff that will talk to customers and help them through the process. They are trying to make the searching process (and fees) make more sense. I think what you are describing may be more of a feature to RedFin than a brand new idea.
I'm not much of journaler, but I think the execution is excellent. Only suggestion: include OpenID or OAuth option for sign up and sign in, so you can have single click access if you want your own account. Should help keep that streamlined feel.
