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Why e is the coolest number



June 18, 2008 – Comments (27) | RELATED TICKERS: E

Okay, this is obviously not going to be a blog about stocks. It will be about investing only in a very general and relatively abstract sense. But growth (and more importantly exponential growth) is why all of us are investing in the first place. And it is interesting to think about the fact that all exponential growth has its basis is one very cool number: e.

Why am I writing this? Who knows, binv271828 is a strange character. But a few of my Caps comrades have wondered about my strange screen name. I really wanted to share why I like the number e so much that I did put it in my name and why it is related to investing.

Let me warn you now that there will be a lot of ideas, mostly math based and some very uninteresting except to those that really like math. Please feel free to skip, and I won’t be offended :). So, it should be abundantly clear to anybody who has read my pitches and blogs that I am a fairly large nerd. I like math… a lot. Numbers are cool. But the relationships between numbers and how they describe physical phenomena are even more interesting.

E is a number that describes a whole class of relationships like this. But if you read a math textbook or looked up ‘e’ on wikipedia you would have no idea how universally cool it is. So here is the dry definition: e, also called Euler’s number, is a transcendental number that is approximated by 2.71828182845904523536. …. Okay, who cares. So here is some more dry definition: the mathematical constant e is the unique real number such that the function e^x has the same value as the slope of the tangent line, for all values of x. … again, who cares!

Okay, lets see why e is so cool.

Everybody is familiar with compound interest. You begin with a starting amount of money, and then you earn interest. The next period you earn interest on the principal + interest from the first period, and this continues until you are rich!

So lets you have an account where interest is calculated once a year. So the growth comes in yearly chunks. If you start with $1 and you get an interest rate of 100%, then at the end of the year you will have $2 (the interest earned on 1$ with a rate of 100% is 1$, and $1 + $1 = $2). Well, what if interest was calculated once every half year. Then that means after 6 months you will earn $0.50 (100% interest for half a year, or 50% earned on the $1) for a total of $1.50, then at the end of the next 6 months, you will earn interest on $1.50. This interest is 50% (for half a year) to give you $0.75. Add back to the $1.50, which gives you $2.25. Right on, so calculating in more intervals gives you more money. So now you have 2 payments instead of one step at the end of the year. Next imagine the interest was calculated once a month, or once a day or once an hour or once a minute or once a second or once a nanosecond…. What this does is to increase the number of steps, which makes your growth curve “smoother”. Eventually with an infinite number of steps in which your interest is calculated, your interest growth will represent a continuous curve.
That is an interesting relationship. And this relationship can be expressed as: (1 + 100%/n)^n where n is the number of steps taken. So lets list this relationship for an increasing number of steps:

Steps       Growth
1                2
2               2.25
3               2.37
5               2.48832
10              2.59374246
100            2.704813829
1000           2.716923932
10000          2.718145927
100000        2.718268237
1000000      2.718280469
10000000     2.718281694
100000000   2.718281786
1000000000 2.718282031

And as you can see, the relationship begins to converge, and lo and behold, it’s e! So this is where e comes in, it is this idea of continuous growth.

What this actually is, is a limit. Okay, I am going to throw some calculus at you. e = limit as n goes to infinity of (1 + 1/n)^n. This is an exceptionally important relationship very useful in describing all kinds of phenomena, and has some very unique properties in relation to derivatives and integrals (more in a minute).

What is even more interesting is that if you start looking at any exponential relationship (interest calculated at interest rates other than 100%, population growth, cell division, bacteria replication, etc.) you can express it as function of e. Absolutely any exponential relationship at all. What this means is that every single continuous growth relationship in existence can be though of as a scaled version of e…. ! How cool is that!

So all of us are looking for continuous exponential growth in our CAPS scores and our portfolio returns :), e is always on our minds subconsciously.

Okay so that’s cool, so what’s up with all derivative and integral stuff? Because of the shape of this exponential curve and remembering the original dry wikipedia definition “the mathematical constant e is the unique real number such that the function e^x has the same value as the slope of the tangent line, for all values of x” an interesting property is discovered: The derivative d/dx (e^x) = x. This is very useful in casting functions for linearization.

Another concept as to why e useful is in the concept of imaginary numbers. It can be shown that e is actually a trig relationship (sines and cosines) in the imaginary domain. Now that is really abstract, but you can think of imaginary numbers as describing an oscillating signal or motion. Any motion that can be described as a magnitude and an angle or phase (such as a pendulum moving back and forth, a wing vibrating through the air, a cesium atom moving back and forth in an atomic clock) can be though of in terms of imaginary numbers, which then can be compactly represent in one number: e …!

E also has usefulness in integrals. Since e can represent imaginary numbers, it can represent any oscillatory signal. Any oscillating signal can decay (think of a bar door when you open it, rocking back and forth on its hinge until it eventually comes back to rest), stay stable or it can grow (if you are not familiar with the bridge “galloping gertie” check this out and be sure to watch the video under the collapse section). So growing oscillating signals are bad for mechanical systems, like galloping gertie, and are also bad for electrical systems. Exponentially growing signals cannot be easily described since their integrals do not converge. So you cannot even analyze the effects of a system with a non-coverging integral.

That is until you throw in some e! Since e is actually an oscillatory number, you can add a sufficiently large amount of negative e in order to force an integral to converge. This is the principle behind the LaPlace transform. Figuring out the size of negative e added can tell you something about the stability of a system, and is a very useful technique in controls.

E is just so cool!

Okay, okay enough geeking out. If you want to use e for some useful formulas for investing calculations, here are a few:

growth = e ^ (total rate * time)
annualized growth rate = e ( ln (total return multiple) / number years ) - 1
where ln is the natural logarithm (another cool relationship that is related to e).

If you also have a love of e, please feel free to share! If you have skipped everything in the middle and come down to the end, well I don’t blame you :)

For more reading on e, check out:

27 Comments – Post Your Own

#1) On June 18, 2008 at 9:38 PM, adventurerneil (20.18) wrote:

Nice to see a math nerd on the Fool. :)

I did skip a good portion of it, but have seen that bridge video before - so cool.

Keep up the posting and Fool on! 

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#2) On June 18, 2008 at 9:43 PM, binv271828 (< 20) wrote:


Thanks! I really appreciate that. Fool on!

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#3) On June 18, 2008 at 10:25 PM, anchak (99.90) wrote:

Hmmm...there ought to be a strange attraction amongst geeks.... now I get what B-inv(exp) is all about ..... Do you have anything against Π ( Your profile statement) Hopefully not.....Would the next one be on Fibbonacci series?

If you appreciate pi - I do it with trepidation on the Fool ( this seems to be mumbo-jumbo at first) ...need to take it with a FIST of salt...


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#4) On June 18, 2008 at 10:30 PM, ajm101 (< 20) wrote:

e^i(pi)=-1 might be the greatest math fact ever.  I was more on the theory side than the applied side, so I never knew what a LaPlace transform was.  Great explanation!

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#5) On June 18, 2008 at 10:50 PM, JustWokeUp (89.58) wrote:

LaPlace transform... Yum... sounds like a great French restaurant :)

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#6) On June 19, 2008 at 12:11 AM, vicpicks (< 20) wrote:

Le sigh* .. I know nothing about math, and tried to follow along.

I do use some tool indicators, like RSI, to help me with stock picks or ending them, but trying to use some sort of math formula, no way.


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#7) On June 19, 2008 at 4:52 AM, binv271828 (< 20) wrote:

Wow! Awesome! I had not expected such a response!


Yes, there are all kinds of strange attractors in the unviverse. Caps happens to be one of them :) yuk, yuk. and LOL. I have nothing against pi (the symbol), nor pie (the food). My profile was quoting one of my favorite Simpson's scenes :)

Pi is excellent, but e is just so much more important and underrated. I just wanted to show e a little love :) That was an intersesting article, where did you find it?

As far as Fibonacci series (which are very interesting), jester112358 probably has a more invested opinion :)

Thanks a lot of the comments!


Thanks! Yes, I defintely agree, that is the coolest math fact ever. I love it! The fact that the two most important trancendental numbers are related is incredible. I just love the idea behind e in the imaginary domain is really sines and cosines (circular motion). It's all connected!

And thanks a lot! Yeah, I had a teacher literally just spouted off, F(s) is ithe integral of e^jwt*f(t)*dt and then proceeded to build a class off that relationship without ever telling us what it meant! So dumb, I hate it when there is no explanation. It was only later that another teacher explained how it was related to a class of problems (non converging integrals in signal theory) and was a covenient way to force convergence, and that the amount of e actually represented some physical quanity.

I like good explanations too :)


HA! That's awesome! That shound be a French restaurant. All the dishes could be plays on the names of French mathematicians! Thanks!


:) No worries. If you come away with nothing more than 'e is a cool number', then the post did its job :) Thanks!

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#8) On June 19, 2008 at 7:49 AM, madcowmonkey (< 20) wrote:

So you are an engineer. I love the different areas of math that e pops up in. It really is underrated. Nice write up.

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#9) On June 19, 2008 at 10:11 AM, ATWDLimited (< 20) wrote:

e, it is natural log too. My favorite equation is (e^(π i))+1=0.

 That is i, as in square root of -2, times Pi, as a power of e.

Pretty crazy stuff, but useful, like Caps

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#10) On June 19, 2008 at 12:24 PM, binv271828 (< 20) wrote:


Yep, I am a mechanical engineer and I work in the aerospace industry, mostly on satellites. Yeah, e is the best :) Thanks man.


Thanks! Yeah, ln(e^x) = x and e^(ln(x)) = x. Yes, that is also one of my favorite equations. And acutally i is the square root of -1. But imaginary number theory is so useful for describing anything with frequency content. It just just so cool that there are so many dimensions of numbers, you can have numbers in the real domain, then in the imaginary domain, and then in the LaPlace domain. It's all levels! :)

Thanks man, yes it is all crazy. But that's what makes it fun! Just like Caps :). As always, I appreciate your feedback!

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#11) On June 19, 2008 at 1:59 PM, Tastylunch (28.72) wrote:

I was always felt bad for ppl I knew in high school who'd say they'd never use math (specifically calc) again in their life.That's kinda like admitting you are going to be stupid and possibly poor for the rest fo your life just cause you are lazy . :-)

 fun stuff binv, gives me calc flashbacks.

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#12) On June 19, 2008 at 2:05 PM, eldemonio (98.06) wrote:

Great post.  You have inspired me to hunt down an investment that calculates interest every nanosecond.  Know of any good options?

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#13) On June 20, 2008 at 5:17 AM, binv271828 (< 20) wrote:


Yeah, I know what you mean. Math may not be everyone's favorite subject, but it is so useful. To just give it up completely is like handicapping yourself. It doesn't make a lot of sense.

Thanks Tasty! I hope the flashbacks were not all bad :)


Thanks! I don't know any good investments right off, but if you find one let me know :) Hmmm... maybe Nanosolar, maybe they will pay dividends every nanosecond .... yuk, yuk :)

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#14) On June 20, 2008 at 11:31 AM, leohaas (29.81) wrote:

Good to see a math geek on CAPS. Quite a relief from all the doom-and-gloom and political posters. Just 2 remarks:

"But growth (and more importantly exponential growth) is why all of us are investing in the first place."

All growth is exponential! Isn't that the gist of your blog? And it is exactly why the only reliable stock charts are on a logarithmic (rather than linear) scale...

"The derivative d/dx (e^x) = x." 

Shouldn't that be: The derivative d/dx (e^x) = e^x?

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#15) On June 20, 2008 at 12:41 PM, binv271828 (< 20) wrote:


Thanks! Everybody needs a little geeky math once and awhile :)

All growth is exponential! Isn't that the gist of your blog?
Exactly! Absolutely all growth functions are related. That was just a little editorializing on my part to hook the reader at the beginning :) Any blog about math needs as much framing as possible to be interesting :)

Shouldn't that be: The derivative d/dx (e^x) = e^x?
Indeed! Thanks for keeping me honest. I am sure I have several mistakes in my post. I was excited to write it, but I was in a bit of a hurry when I wrote it :)

And I agree, log plots are always the best way to go. Whether looking at Stock Charts or Frequency Response Functions :) (a little dumb structural analysis humor) Thanks again!

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#16) On June 21, 2008 at 8:54 AM, madcowmonkey (< 20) wrote:

Here is the recipe I had mentioned.

1 cup onions

4+ jalapenos

1 bunch chopped leaves of cilantro

4 cloves garlic

1 peeled cucumber

6 stalks celery

2 cups clamato

2 cups spicy V-8

juice 2 lemons

juice 3 limes

2 avacado

1 lbs. shrimp cooked, peeled, de-veined, no tails

 Fine chop everything but the shrimp and avacado. Mix in a bag or bowl and add salt and pepper to taste. Let it sit in the fridge for at least one hour and then buy some tortilla chips and some dos equis and go to town.

Wow. leohass did a derivative check on yo ###. That is funny, because it was the easiest one:)

Have a good weekend. I will be at the beach, after house work of course. Got to get the place ready for 40+ people next weekend. Hamburgers and deer brats all the way. Now I just need to pray for good weather. 

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#17) On June 21, 2008 at 10:47 AM, binv271828 (< 20) wrote:

Awesome madcow, thanks for that. That does sound good! Mmmm.. Dos Equis. I do believe I have to have a few of those this weekend :)

Yep I got schooled :) I should have checked my d/dx before I wrecked my d/dx.... ahhhhhhhh. Ya gotta love math humor.

Have a great weekend my man. Which beach you headed to, Petosky? Charlevoix? Do you live that far north? Yeah, and I am hoping for good weather for you next weekend. Us too, we are heading to North Carolina. :)

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#18) On June 22, 2008 at 10:16 PM, madcowmonkey (< 20) wrote:

We use to go to Petoskey State Park when we lived in Petoskey last year, but now we live in Boyne City (less traffic lights :) and what seems to be the most popular state park is now Young State Park. It is on Lake Charlevoix about 2.5 miles from downtown Boyne on the way to Charlevoix. I still really like the Petoskey beach when the waves are coming in, but it seems to be so windy when we go. We had great weather this weekend and spent 7 hours at the beach and did lunch and dinner. Plenty of kids running around and the moms are hot:) I hope we didn't blow our load on the weather for next weekend. 

What part of NC are you going to? I met my wife at the Nantahala Outdoor Center when I worked as a raft guide, bus driver, cook, and party animal. The Smokey Mountains are really fun and if you are in the area and you like to hike (kids old enough) go check out wildcat falls. Very secluded and picturesque. Watch out for the river when it rains though, we almost got caught in a flood. Good thing my wife is a smart camp ground picker, right next to the river:) It is an overnight hike, but it is worth it if you like to be alone. 

I just found out my wife's family will be coming up, so strike that first number and add another 10 people to make it an even 50. I had to ask the neighbors if I could borrow their grill. Ahhh. Good times:)  

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#19) On June 22, 2008 at 10:31 PM, binv271828 (< 20) wrote:

Awesome! Yeah I love the Northern LP on the Lake Michigan side. At the cities and towns are great. Very fond memories of Petosky and Charlevoix. One of my first trips up there was a camping trip with my parents. And we had a few Petosky Stones before we went, all polished so you could see the fossils. So we were eager to go stone hunting. Well as soon as we get to the camp site my Dad reaches down and says "Hey I found a Petosky Stone!" And we are all like "let's see!" and it is just some random rock with no fossils and he shrugs his shoulders and says "well, we are in Petosky right?" ... yuk, yuk. So you can see where my droll sense of sense of humor comes from.

Dude, you have been to Nantahala?! That is great. Actually it is a big forest. Yeah, my wife's parents live down there. A small town in the mountains kind of near Asheville. It is called Cashiers and it is right in Nanathala. Man I love it there. There is so many hiking trails and so many waterfalls. Wildcat falls is not ringing a bell, but our favorite hike is down to Whitewater falls. Beautiful! Have you ever rafted / canoed down the Ocoee?

Whoa, that sounds like it is going to be a kickin party :) Nice :)

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#20) On June 23, 2008 at 7:24 AM, madcowmonkey (< 20) wrote:

Your dad sounds cool. My wife and I use to take snorkels out and look for the stones. She loves that stuff, I just like to get in the water and hang at the beach. I am not very good at finding them, but she is always spotting them.

I had heard of Cashiers, not sure if I had been there. We almost moved to Asheville. I like the music festival that they have there, some french name I can't remember right now. The Ocoee. Did the raft thing with my wife and some friends. I paddle too, so I did the white water kayaking. I also did two trips with a white water canoe. The first experience in the canoe was a little ruff, but the second was really fun. I like Hell Whole, but there are some really fun play spots along the way and Hell Whole gets too many "showboaters", i am not into that. I like having fun. 

I worked at NOC for 4 years. 2 were as a raft guide, but I got bored of it plus the sun was taking its toll. The other 2 years, I was a bus driver and cook.

Wildcat falls is actually in the Joyce Kilmer forest I can't remember the directions to get there, but you could probably look it up. 

Do you paddle/yak/boat? How old are you? VA has some great rivers too. I have been working on getting a new kayak for the waves in Lake Michigan. We have two boats, but they are outdated and I have put on about 30 pounds since the last time I went boating on the river. I really like surfing on the lakes, but I miss the white water and all the people that are in the sport. Nice thing about the Nannie is that it keeps the Gorge cooled off in the summer.

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#21) On June 23, 2008 at 8:32 AM, binv271828 (< 20) wrote:

Yeah, that whole area is awesome. It really is a weird small world: Michigan, North Carolina, California and Chandler, AZ. What are the odds :).  I am 32. Yeah VA does has some nice rivers, but I really have fond memories of Tennessee and NC rivers. I will look up Wildcat Falls and see if it is on the way down. Thanks man!

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#22) On June 23, 2008 at 10:57 AM, madcowmonkey (< 20) wrote:

It isn't a hike for kids. The hike in is easy (all down hill) but the hike out was a little tough, especially with the humidity. 

So do you kayak?

I need to send you an email, this is starting to look like a caps love affair:) If you kayak of course.

How old are your kids? 

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#23) On July 18, 2008 at 1:31 AM, TheGarcipian (34.40) wrote:

Hey B-inv(e),

I'm a little late to this party train of responses, but I'll take your LaPlace and raise you a Fourrier transform, if you don't mind the signal attenuation!

Cool write-up. Before reading your reply (#10 above) to madcowmonkey, I guessed you were (in this order): Mechanical Engr., Civil Engr., or had an advanced degree in Mathematics. Why in that order? Because the application of signal convergence was mentioned (which pretty much ruled out the CE), but mostly because if you'd been a Math Mutt, you'd left the work for the rest of us to do as an exercise! Yuk, yuk, yuk. Wait, wait, lemma go! I'm just getting integrated...

From one M.E. to another, that was a good explanation of e. And I learned something too: the application of e to force signal convergence, as well as the oscillatory nature of e in imaginary space (sines, cosines). So what did the Torus say to its Hole? Something like "I'll see you in Imaginary Hell!"

Of course, the biggest problem with the application of e to market forces is the bad assumption that the stock market is (a) linear, (b) exponential, (c) well-formed, (d) continuous, or (e) even rational(!). But the log charts definitely do help seeing the picture more clearly, and I do get your point: If (and that's a big if) we can remove some of the non-continuity of the n-dimensional curve into (n-1) dimensional space, we would have a better chance at spotting trends. Any ideas? If any pan out and before you trounce Buffett, please share!



P.S. I don't kayak but I have a long-time friend who lives near Jonesboro, TN, and gets out to the Ocoee at least once a year. He swears by that river, just loves it! I've seen pics; it looks lovely, beautiful and awesome in its raw nature.

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#24) On July 18, 2008 at 7:00 AM, binv271828 (< 20) wrote:

Gar, Hey man, no worries on the lateness, I am glad you hopped on board!

LOL! Man math humor is the best! Your comment on "leaving the rest as an exercise" reminds me of a cartoon. There are two professors standing at a chalkboard and there are a ton of equations on the left side and the right side, but in the center is written "then a miracle occurs" and the caption reads "I think you need to be more explicit in step 2" :) Good times :)

You're an ME too! Excellent. So far that make me, you and masterwill. Come on everybody, MEs of Caps unite! Yeah, I was glad to share (or geek out as the case my be) about some of my hard-won realizations about e.

Yeah, there is so many cool math tools that can be applied to signal theory (and I sometimes try to look at stock charts as signals). But really I have to agree with your a-e realizations above. Stock behavoir is usually not many / sometimes not any of those. It is almost better to approach technical analysis from a statistical manner and maybe you even have to be heurisitic. It is so irrational and there is so much manipulation. You either have to guess and be right about key long term trends, or get very lucky in the short term :). But definitely, sharing is par for the course here on Caps :)

Yeah, western North Carolina, South Carolina, north Georgia, and east Tennessee. All of that area is just so awesome.

Thanks for the comments! I really appreciate them man!

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#25) On July 18, 2008 at 8:37 PM, TheGarcipian (34.40) wrote:

Taking your cartoon to SouthPark's boundaries and to see how it can be applied to investing, I'm reminded of the episode where the Underpants Gnomes steal Tweek's underwear and lead the Boys into their lair where they must explain their business plan. First step: "Collect Underpants". Second step: "Do Something". Third step: "Profit".  Hilarious!  Like those gnomes and many others, I am still working on Step #2...

Unfortunately, it wasn't until my advanced math courses (either late in my Bachelor's or during my Master's work in M.E.) that a real practical example of how higher-order math could be applied (outside of velocity & acceleration & kinematics calculations) was finally given: Fourier transforms for frequency attenuation (if my memory serves me correctly) and partial differentials. Those were such eye-openers! And it also highlights my biggest beef with the Math Herd: Dudes, get your Eigenvalues out of your Bessel's Equation and talk some practical sense, will ya? And what's with the four-pocket shirts, anyway?! Did the Goodwill have a sale again? Ah, bet you didn't notice they sell combs too, huh?

Math could be so much more fun and informative, but math afficionados are usually the worse teachers. I'm glad I'm an engineer...

My master's work took me into Computer Graphics and, specifically, Man-Machine Interaction & Communication. I took a course in Graph Theory (Konigsberg problem, anyone?), and though I struggled with the format of that class, I really loved it. It helped us write software that converts 2D rectilinear sketches into full 3D objects without the use of geometry.

If that slipped by you too fast, it's OK. Most people don't get it. But I'll say it again: converting 2D images (having only X & Y coordinates) into full 3D objects (X, Y & Z coords) without the use of any dimensional or directional numbers (no geometry whatsoever).

It was/is a really cool field. Provided you don't have any holes (ala, the aforementioned Torus) in the subject, you can do this conversion using graph theory and some face recognition software written by my colleagues at LSU. Imagine if you drew a block letter "M" on graph paper in a wireframe format and gave it some depth (note: a block letter "B" or an "8" would have two holes in it, which we can still do but they require a little bit of geometrical help to point out the inside/outside of the frame). Anyway, the "M" would essentially look like a 3D object but it's embedded in a two-dimensional space (your paper). Our software could convert that to a full three-dimensional object in memory, understanding its "inside", its "outside", and the bounding surfaces in-between. Once the object has been converted to 3D, some geometry could be applied to it for the sole purpose of converting those faces into recognizable surfaces (this is a plane, this is a cylindrical surface, this is a Bezier surface, this is a quadratic surface patch, etc.). Then you can render it for viewing, but that geometrical info supplied does not take away from the fact that the object's inside and outside were already known by the application of graph theory and face recognition algorithms.

And unlike the Math Nerds I teasingly denigrated a few paragraphs back, I will provide a real-world example!  When you have time, check out Google's SketchUp program. It's free software out of their Boulder, CO, office, and I predict you will see more and more of this type of information in the next 5-10 years on the Web. Part of this program is to take two-dimensional building footprint information retrieved from satellite photos like you see on Google Maps and extrude it into 3D, then apply several slightly-off-the-straight-down views of the same building (complete with shadows), and merge them all into creating a wire-frame representation of that building. I believe some of the software that I used in my Master's work at LSU (but not written by me) is being reconfigured to serve this purpose for Google (I have a friend who has a friend...).

But what's all that good for? In the next 5-10 years, in addition to seeing street-views like we can see now in Google Maps, you will be able to see a complete rendering of the actual buildings that reside at the address of interest, completely to scale and capable of having volumetric calculations performed on those buildings. You will (almost literally) get to see what your destination looks like when typing in an address on the Web before you take off for that destination.

Pretty cool stuff, huh?!


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#26) On July 19, 2008 at 9:01 AM, binv271828 (< 20) wrote:

Gar, that is awesome! I forgot all about that Southpark episode. Good stuff.

And I agree, I am a glad to be an engineer too. I love math, but I disliked how all the math professors treated calc / diff-e / partial-diff, etc. as just rote concepts. I want to see how this stuff is useful. That is why I like a field like aeroelasticity. There is still so much applied math, with concepts like the Theodorson function which is applied Bessel functions to describe simple harmonic responses of airfoils with respect to normalized parameters, and then right along side of it is Computational Fluid Dynamics to take an empirical result from the Theodorson solution and propagate numerical results. It is so cool that even today a lot of the CFD codes rely on both. It really gives an appreciation of how these complicated problems were solved before computers, while still combining all of the advancement / usefulness with computing power today.

Your field is an awesome field man. I am a bit of a programming nerd myself, so I can appreciate what you are talking about. But it is fascinating to think how the format of 2D information can inform how a 3D object should be represented. That is really wicked cool. I have seen the demonstration / concept of what you are talking about, how the 2D satellite pictures can be turned into a 3D representation in Google maps. That was one of the coolest things I had ever seen and am I so psyched to see that this will be going mainstream. You definitely have a very cool job in a very cool field!

But if you will allow me to wax metaphysical for a minute, this really reminds me of something else. This is a bit like holography in the sense that 3D information is encoded on a 2D surface. I don’t know if you like to read stuff like “A Brief History of Time” or “The Universe in a Nutshell” by Dr. Stephen Hawking, but he talks about the fact that some theoretical physicists think of our universe as a holographic universe. That the dimensions that we see / experience / measure are simply a representation of “information” on a membrane. This is one of the thoughts behind brane theory.  So wheras string theory has extra dimensions that are higher order and very small beyond our perception (and tiny particles wink in and out of existence through these “small” dimensions), brane theory posits that the universe is composed of adjacent membranes that are very close, and that that these high speed particles have enough energy to move between branes, which is why they seem to wink in and out of existence. But the brane theory goes a bit farther in how it tries to explain gravity. Gravity is by far the weakest of the four basic forces in the universe, and nobody really knows why. Brane theory says that gravity is actually a strong force, but it is shared among these adjacent membranes and so that is it appears weak on “our membrane”, because it is only a fraction of the overall universal gravity … :)

Who knows if all or any of this stuff is right. But it is fun to think about :)

But the real point of bringing that up is that math / physics / engineering are all related, but moreover that the more we discover, the more that all of these areas are influencing eachother. We could never have replicated a hologram hundreds of years ago. But what turned out to be a very interesting physics / engineering experiment is now shaping how theoretical physicists view the cosmos. The more we discover and explore, the more we expand our understanding of existence.

… . Okay, maybe that was a bit too “out there” for Caps. :). But your work is so cool, that it just forced me to go on my tangent. I will definitely be checking out SketchUp this weekend :) Thanks for all your feedback and sharing, that is all great stuff !!!

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#27) On July 24, 2008 at 2:23 AM, TheGarcipian (34.40) wrote:

Hey BinvE,

Yeah, I think if anyone else has got this far reading our drivel that they're probably screaming out for the Nerd Police. LOL. Others might cry out, "Get a room!" LOL. Still, funny how minds think.

Clarification: It's hard to be concise in a blog and not totally lose people, so I want to make sure I didn't mislead you. That field of software (2D-to-3D graph theory) was back at LSU, useful when I was getting my Master's. I'm not in that field anymore, but am still very much in the software and CAD field now. As a consultant, I get to wear a lot of different hats, all in the cabling & harness fields: software development, training, doc writing, process assessment, process improvement, installation of our tools, sales support, product/tool improvement, collecting customer feedback, etc. We help people build wiring harnesses for planes, trains, automobiles, trucks, tanks, and even snowmobiles. The consulting job has given me a chance to travel all over the USA, to Germany, England, Sao Paulo (Brazil), Singapore, Penang (Thailand), and Hong Kong (in a typhoon no less!). Travel has its advantages, but it gets old, and hotel life sucks. This week, I'm in Detroit working with some automotive people. On the plus side, I've got to see some pretty cool assembly lines, from Sikorsky's BlackHawk helicopters, to Germany's EuroFighter jets, to Boeing's multi-million dollar flight simulators, and all manner of planes/cars/trucks in-between. 

Unfortunately, I don't get to write computer graphics software anymore (but I fully understand the transformation matrices involved and can matrix-multiply the crap out of a robotics system, at least in my mind!). I had to be a bit vague earlier because I don't want anybody at Google getting in trouble (not that I think anything I've written is proprietary, but you never know). I hope their SketchUp tool is a total success.

Finally, yes, I have read Hawking's "Brief History of Time" and it blew me away. I didn't follow the latter chapters, but man, that dude is out there! I really loved his PBS series on the universe as well. Very cool stuff.


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