Fun with Orthogonal Transformations

An orthogonal transformation is defined well at Wolfram's Math site. Essentially it transforms one Cartesian basis to another.

Consider the constraints placed by the Kronecker delta:

$\delta$ij=ei·ej=[∑(ei·ek')ek']·ej=∑(ei·ek')(ek'·ej) over k

Define
$a$ij≡ei'·ej


$\delta$ij=∑(ei·ek')(ek'·ej)=∑akiakj over k

There is of course a similar set of relations:
$\delta$ij=∑aikajk over k

They place 0.5n(n+1) constraints over n-dimensional transformations, leaving 0.5n(n-1) degrees of freedom.

Einstein Summation Convention Found Annoying

Maybe I don't have the mind of a physicist, but I am finding Einstein's Summation Convention to be very annoying. I can (sort of) see how it may save a publisher space, or a writer time. But, for a layman reader, like myself, the convention means every equation may be interpreted at least a couple of ways.

My Appetite for Physics Has Returned

I am never reading just one book at a time. I get interested in other stuff at the same time. So now it seems like, after a long hiatus, I have returned to one of my early favorite subjects, physics.

Unfortunately, I am so rusty, that I need a refresher. So I got out my copy of Mathematics of Classical and Quantum Physics, and will be doing some review.

Physicists look at the same Mathematics as Mathematicians in a different light, so even reviewing their vector notation may be in order.

Trying out News Feeds

You will see a lot of news on technology and stocks (and some other random stuff) now.

"Left Brained vs. Right Brained" Nonsense

Why are people so down on the left brain?

Is it to make up for the older times when the right brain was denigrated?

The left brain gives us analysis, without which, creativity would be an empty shell.

Michaelangelo, da Vinci, and many of our great artists were quite analytical as well as creative. Both had some background in the sciences as well as the arts.

Analysis without creativity should be left to the computer. Programming is a different matter.

It seems like only people who haven't programed a lot believe programming to be a purely left-brained activity.

There is a similar thing with Math. Not until you take an "anything goes" approach to touching upon the key ideas of a Mathematical proof, and watch them work out in logical splendor, will you appreciate all the beauty there is in Math. It is necessary, but not sufficient to do so :)

How do you spot a scam?

I've been getting a lot of calls from people offering opportunities for business. The first step is always either free or very cheap, and the information comes in small book form or an initial seminar.

The next step: when you got said seminar (often free) you get pitched high-priced offers to do other programs.

At the other programs they will present some information, but pitch still higher priced things.

The activities tend to be semi-legit things...

Tax-liens/Tax Deeds, real-estate education, stocks, options, commodities, legal advice, grant writing help, auction web-sites, whole-sale drop-shipping, cash-flows, various MLM programs, and many more...

I am sure some of them actually worked. I've indeed used one of the stock tools to good effect. I have recovered the money I spent many times over, and their tools are very rich and powerful. But I wonder if the stock tool was a fluke, and if maybe that experience has primed me as a sucker for other such deals.

If you think about it, these aren't very different from the exercise equipment, and fad kitchen devices. If you are actually going to use it and make it work, then it may not be a rip-off, but we know that most of that crap will barely make it out of the box. I wager, this fact is known also to those selling the products.

Are they scams though? There are so many reports on Sears, Disney, and other such companies on Rip-Off report. There will always be unsatisfied customers.

I am unfortunately a sucker for such things (kind-of soft-spoken, and seeking a better life), but I managed to say no this time. Eventually, I would like to string some of these schemes to the point that I have replaced my regular income, and eventually to be financially free.

I'm thinking it may actually be easier to pitch my idea to VCs and get rejected 100s of times till I get an idea that sticks. It somehow feels more legit.

Why I am like Captain Ahab

My Current Obsessions

• Greatness (I know, the arrogance)
  
  • I want to be an amazing something
    
    • 1) A great inventor
    
    
    • 2) A great scientist/mathematician
    
    
    • 3) A brilliant business person come philanthropist
    
    
    • 4) World class at something difficult


• Peace of Mind
  
  • I want that deep peaceful and powerful concentration I used to have as a kid
  
  
  • I want to be able to think deeply about a subject with patience and trust that the process will be fruitful


• Being Inspired/Motivated
  
  • I want the sense of wonderment to be powerful enough for me to accomplish things
  
  
  • I want the trust that I will have the time and energy to make something constructive from following my curiosity


• Deep Understanding
  
  • I want to understand more things that I am involved with from its constructive "first principles"
  
  
  • I want to be able to achieve this level of understanding in way that seems more volitional and predictable

I Have Some Strange Ideals About Technology

My Strange Ideals About Technology
I want everything tedious/repetitive to be automated
I want every place there is information accessible via a very simple interface
I want to be able to convert all legacy code into modern frameworks
I want every idea to be able to be captured and stored electronically
I want to be able to specify any object and have it made to order
I want energy expenditure to not be a concern (No environmental concerns, No monetary concerns)
I want technology to provide the basic needs for all human beings without the need for them to struggle
I want the scarcity of any resource to not be a concern

I signed up for AdSense

Based on an earlier conversation with LurativeSid, I decided to try out Google AdSense. It seems fairly unintrusive, assuming the content on my site stays OK. I actually like what they are displaying (ads for Earthquake relief, and Social Entrepreneurship. I'm cool with those.)

Energy, Engagement, or Just Getting Things Done

So, I've decided to read three "self-help" books at once.

Getting Things Done
High Energy Living
The Power of Full Engagement

The hope is that I will become more effective, energetic, and engaged.

I wonder if there are any job prospects for the lazy and/or burnt-out.

I don't know hoe I get this low. Lack of sleep yesterday maybe?

I have been having trouble sleeping again. Allergies keep me up. Plus, I'm one of those "long-day"ers.

I'm thinking about what I would do if money, responsibilities, familial concerns were not issues.

I think it's pretty clear that I would go into the renewable energy field. School is not my favorite activity, and I just barely got out of an M.S. with my sanity.

However, a full-time Ph.D. program in Physics, Chemistry or Electrical Engineering, with a focus on renewable energy technologies is the most attractive thing on my mind.

I hate getting up in the morning, and I hate coming in even more. I offered some of my least creative/most conservative suggestions to my technical lead last week (who is very smart, and whom I respect very much) and I was pointed out as thinking "out-of-the-box." This was scary. In my old group, this would have just been taken as a normal good idea.

Big group politics, I guess. All the people can be good, hard-working, knowledgeable people, but the structure itself is so overloaded with red-tape, that making even simple changes that make sense are "out-of-the-box." Sheesh.

Time for me to get out, I think. Either find a more innovative group, or a more innovative company. But moving to a new field, which is just poised to grow, seems like the best idea.

I don't feel like I have the energy to do these projects "on the side." My day job is demanding enough.

I'll keep chewing on it. Being Asian makes the whole family pressure thing very strange.

This blog hasn't been getting much use. So I've decided to lower my standards. I am simply going to start whining, griping, and or posting stream of consciousness type posts on the blog.

I frankly don't see what's great about g-mail, I already have more e-mail addresses than I can remember.

But I will try it out, since it is required to maintain this blog.