Thanks for the clarification! Good luck with the project! Keep us posted on how it goes!

For your

>Sigma, I’m not sure how your post relates to BRC’s subject matter

I was drawing from BRC’s

>This weekend, go to church or temple or mosque and say a prayer of gratitude for having been born into these times.

specifically the

gratitude for having been born into these times.

along with BRC’s theme of actually DOING things, e.g., exploiting “these times” with the shockingly better price/performance to plug together a computer, write some software, say, go live on the Internet, and use those to make money — visit “the pay window”!

I omitted mention of the potential role of some mathematical ideas prior to the computing and where the most important role of the software is to do the data manipulations and, possibly, numerical computations of the prior ideas.

Why “mathematical”? In principle, all data manipulations and everything that software does is necessarily applications of the logic in a computer, is, thus, necessarily logical, and, thus, at least in some sense, and maybe also in a quite strong sense, mathematical. So, for more powerful manipulations, there can be some advantages proceeding mathematically. E.g., via some mathematical theorems and proofs, we can know that some valuable things are true well before we write software actually to give valuable, real versions of those things. E.g., there is

It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can change the course of human affairs.

Stanislaw Ulam

Or, for a block diagram from 50,000 feet up, in computing we take in some data, manipulate it, and report results. Well, to make money, we want the manipulations to send out results that are quite desirable and/or useful and, thus, valuable. When live on the Internet, we want the results to have lots of happy users and, then, run ads that we get from, say, ad networks. And, maybe for each user, we can take some of the input data relevant to that user and do some especially effective ad targeting to increase the ad revenue.

Here is a simplified version of some things I learned in the best courses I took in grad school and have used with good effect in some practical problems:

From some aspect of a person, thing, etc., we observe a number. Call that observation one trial, and call that number the value at that trial of random variable X. So, for one common explanation: The one number we observed is one of many that we might have observed.

Maybe from lots of trials, real or just imagined, for any number x that we might select, we can get the fraction of the observed numbers from random variable X that are less than or equal to the number x we selected. That fraction we call the probability that an observed value of random variable X is less than or equal to the number x which we write as

P(X <= x)

which is the cumulative distribution of random variable X.

So, we might select x = 2 and get

P(X <= 2)

Easy enough to understand.

With that cumulative distribution, and some meager assumptions, especially meager in practice, we can find the long run average value of random variable X, that is, the expectation of X written E[X]. We are interested in random variables X where E[X^2] exists and is finite (that is, is not infinite.

With random variable X, we can do essentially any arithmetic or mathematical operations on the values of random variable X and get another random variable.

Given a random variable Y, we can form the sum X + Y or the product XY and get more random variables. Then we can take E[XY] and get an inner product which is closely related to the cosine of the angle between X and Y. If that cosine is small, then the angle between X and Y is small, and X can be used to make a good approximation of Y. So, in practice, maybe know Y would be valuable; we don’t know Y; but we know some X that is a good approximation to Y; then maybe X is also valuable. The value can come from, say, more accurate ad targeting.

We can treat such random variables as points in a vector space where each random variable has a length, the square root of E[X^2]. We’ve already discussed angles: Well we can show that the classic Pythagorean theorem holds. How ’bout that! We also have the triangle inequality that the sum of the lengths of two sides of a triangle are not less than the length of the third side. We also have the parallelogram equality —

as at

https://en.wikipedia.org/wiki/Parallelogram_law

with

… the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.

Since we are working with vectors, we can consider all the linear combinations of some of them and get something much like an ordinary plane. An ordinary plane has only 2 dimensions; the vectors in applications of linear algebra have finite dimensions; what we have outlined can have infinitely many dimensions.

With the planes we get, we can do some projections. As we can quickly show, all that is required are the inner products!

Projections give us an important case of a closest possible approximation. So, as in the 50,000 foot description above, in some cases we can take in some data we have and do some projections to find the closest approximations to some other data we want. The approximations might be valuable, e.g., for ad targeting.

It turns out, what we have mentioned are some manipulations that were long found powerful in many problems in physical science and engineering. So, we have some tools — like saws, files, hammers, drills, glues — useful for many different pieces of work.

The 20th century mathematician John von Neumann, generally regarded as a bright guy, formulated these tools into what he called, after the famous mathematician David Hilbert from near 1900, a Hilbert space. So, von Neumann gave some axioms for a Hilbert space; then in practice any mathematical example that satisfies the axioms is a Hilbert space where we, then, know that all the tools — Pythagorean theorem, triangle inequality, parallelogram equality, and a lot more — work. So, and this is amazing beyond belief, the random variables we are considering form a Hilbert space.

Well, with the rational and real numbers, we can consider the square root of 2. As we can show easily enough, there is no rational number that is the square root of 2. But we can get a sequence of rational numbers, e.g.

1

1.4

1.41

1.414

1.4142

1.41421

1.414213

etc. that are more and more accurate approximations to a square root of 2. One of the fundamental properties of the real numbers is that such a sequence that appears to converge (technically, that it converges in the weaker sense of Cauchy) really does converge and converges to a real number that really is the square root of 2. This property of the real numbers is called completeness.

Well, a Hilbert space is complete. In particular, a sequence of random variables such as we are considering that appears to converge (technically, that converges in the weaker sense of Cauchy) really does converge to a random variable also in Hilbert space. It is amazing that any such thing could be true, but it is. Just as amazing, the proof is surprisingly short.

So, in practice, with our view from 50,000 feet up, if the data we take in can give us a sequence of random variables that appear to converge, then we can be sure that as we take more terms of that sequence we can approximate the random variable the sequence converges to as closely as we please. In some practical cases, the resulting approximations might be valuable, e.g., provide more accurate ad targeting.

Such projections and convergences are part of the core ideas of my startup to get the valuable results for the users.

Some people would label the applied math I’ve done as artificial intelligence (AI). I call my work solid, likely useful applied math and call AI hype and usually junk.

For my project, to do the computations, handle the data, develop the Web pages, etc., my 10 fingers typed in 100,000 lines or so of software — about 25,000 programming language statements plus about 75,000 lines of in-line comments that will let me understand the code whenever I have to look at it again.

As of now, the software, computations, and Web site all run, or at least did before my current development computer got sick and corrupted some of the Microsoft .NET data my software uses.

The 8 core processor I’m installing will be for more software development and my first server.

The way some back of the envelope arithmetic works out, if via publicity, giving users what they like and want, virality, etc. I can keep the computer on average half busy 24 x 7, then the monthly ad revenue should be $200,000+.

Really the Web site should be of nearly universal interest around the world, that is, of interest to nearly everyone on the Internet. So, with $200,000+ a month of revenue from one 8 core server, there should be much more revenue growth available and plenty of organic funding for more such servers.

Then hire an electrician to put in a bigger circuit breaker box, say, 200 A or 300 A, run some lines to a couple of spare bedrooms, put in some window unit A/C units, get some uninterruptible power supplies for the electronics, and get an emergency generator with an automatic cut over on a hut on a concrete pad out back.

Then get another factor of 10 in revenue to $2 million a month and rent some floor space, flat area, solid concrete floor, good walls and roof, good electric power, good Internet connection, maybe an old shopping mall or factory, and get another factor of 10 to $20 million a month.

Then start to hire and manage along the lines BRC’s has outlined.

Then, take some from “the pay window”.

The next step is that computer I’ve done the shopping for.

Sigma, I’m not sure how your post relates to BRC’s subject matter, but I will chime in about PC building — as you see, I’m an old-timer as well.

My 1st job out of college was selling 286 based PC’s that weighed probably 40 to 60 pounds depending on the config for $2-3k bucks or so. And 30 years ago, that was a fair chunk of change. Throughout my 20’s and early 30’s, the PC biz was an exciting time. The 386, oh my! By the time the 486 came along, there was talk of software never catching up to that kind of bandwidth. And I’ll never forget Apple spending a better part of a decade suffering from manufacturing issues that forever had multiple products on back order, and pissing everyone off. But back then Apple truly had a big operating system edge that people were willing to pay and wait for!

So my whole life, I’ve always built my own box. I don’t think that I ever saved much money doing it on my own, but I always valued picking the best components when I knew the mainstream manufactures most always used inferior components to save $$. And if I made a mistake, or had to spend hours upon hours finding solutions to problems, at least she was MY box. A true Geek would not have it any other way!

Yes, 2TB drives are the sweet spot. A couple of years ago, I tried a 3TB drive and it was a slow clunker and it crashed on me. I’m always sticking with WD and will never ever purchase a Seagate drive again. I’d love to try out an 8 core CPU but won’t pony up a grand for it. In my next build, maybe I’ll pay $125 more for a 6 core if I’m in a good mood.

Take it easy!

.
Real world, real experience. Moores Law. Wow!

BRC
http://www.themusoingsofthebigredcar.com

But the parts available have price/performance, in the context of the past of computing, totally beyond belief. E.g., for a processor for about $140, can get 8 cores (each such core is a little better than a single processor, with just one core, used to be) that uses 64 bits to address main memory (up from 32, 24, 16 in the past) with a clock that ticks (much like a metronome in music) 4 billion ticks a second. The last IBM water cooled mainframe I knew about when I was at IBM had a clock that ticked IIRC 153 million ticks a second. So, let’s see, 4 billion divided by 153 million is

4000/153 = 26.143

This 8 core processor is about one square inch and less than 1/4 inch thick. The IBM thing needed a fork lift, a raised floor, and a source of chilled water and had maybe only one core instead of 8 and cost ballpark $1 million. So the performance ratio is about 8 * 26.143, and the price ratio is about 1 million over 140 for a price/performance ratio of

(10**6 / 140) * (4000/153) = 186,741

Not bad! Who’d a thunk that?

But, wait, there’s more! For disk storage, at one time I led an effort to get a disk drive with 300 million bytes, the size of a washing machine, shipping weight 750 pounds, for about $40,000. Now can get 2 trillion bytes (TB) in a package the size of a sandwich for $70. So, the price/performance ratio is, in whole numbers,

(40,000/70) * (2 * 10**12) / (300 * 10**6) = 3,809,524

Gee, that’s a lot better than even the processor price/performance ratio!

The progress has continued: (1) Internet access at 25 million bits per second up to 1 billion bits per second instead of dial-up at 300 or 9,600 bits per second; (2) operating system software; (3) infrastructure software, e.g., programming language compilers, libraries of open source software, utility programs, relational database software, TCP/IP stack, e.g., for Internet access, Web software, social media server sites, and much more; (4) 1+ billion people on the Internet; and more.

Somewhere in here we should thank the people who did error correcting coding, e.g., Hamming, Reed, Solomon, Viterbi, etc.

There should be some ways to make money from all of that!

http://themusingsofthebigredcar.com/iq-v-will/

And?

BRC
http://www.themusingsofthebigredcar.com