Archive for October, 2007

Human Mathematics

October 7, 2007

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Human Mathematics: Archive

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December 2010

29 posts

10 tags

Dec 16th

8 tags

Dec 16th
1 note

8 tags

High-Frequency Trading
The point of high-frequency trading is to smooth markets over time.
Imagine that you know a big block order is coming in. Some huge pension fund needs to send 70,000 checks out next week so they’re selling some asset.
The asset’s price doesn’t really deserve to go down. The fund just wants to cash out. So you buy the huge block order and dole it out in smaller pieces as regular…
Dec 16th
1 note

4 tags

Shorts
What’s the point of short-selling? To take money away from those who have too much.
US stock market capitalization is roughly $7 trillion. So all of those trillions of dollars are in public companies and not somewhere else. Maybe that’s bad.
Shorting a company is a vote against them. The CEO might say it’s mean, but maybe somebody else’s project is more worth funding than…
Dec 14th

10 tags

Finance Week →
A series of short “What’s the point?” pieces about leverage, stat arb, shorts, value investing and all that forthcometh.
Warning: this is all stuff that an economist would say, not stuff that a trader would say (unless the trader was doing PR).
Dec 14th
2 notes

5 tags

The Point of Finance
The social end of finance is to make sure society’s money is going to the most worthy projects. In technical terms, to equalize the risk-adjusted marginal return on capital across projects.
(Of course, if “worthy” is measured solely in pecuniary return, then much is missed. That’s why economists want externalities to be priced into the market.We hope to make The Good = The…
Dec 13th

6 tags

Dec 13th
2 notes

6 tags

Dec 12th
4 notes

2 tags

Dec 12th
4 notes

10 tags

“No computerized calendar, log, scribble-pad, or time-tracking tool works as well…”

– A. Grimm

Dec 11th
9 notes

6 tags

Freshbooks vs Smartecarte

The above websites are all suspiciously similar — not made by the same person, but by the same culture: web developers. Fact:

All of them claim to be “the easiest way to send invoices online”.

I believe the logic behind developing these products must have gone something like this:

Kind of like the underpants gnomes from South Park. I can imagine the conversations…

Dec 11th

5 tags

ListenO.N.E. by Yeasayer
Dec 11th
12 notes

8 tags

Read Before You UpVote
This is a suggestion for Reddit, Hacker News (ycombinator’s), and other Digg clones.

Only count up-votes from people who have clicked through to the article.

The flourishing of voting communities is a blessing to the Internet. Members post links and everyone gets to vote up or down. It’s an improvement on Google’s PageRank, which has been maliciously exploited by spammers…

Dec 10th
1 note

8 tags

Dec 9th
11 notes

6 tags

ListenMaria in Motion by Son, Ambulance
Dec 9th
2 notes

8 tags

Vierergruppe
Any four things in order ABCD can be rearranged. You could do

ACBD — middle swap — 1324

DBCA — end swap — 4231

BCDA — rotation — 2341

for example.
Let’s say the four things are the four corners of a square. That’s valid, because ∃ a functor that maps {rearranging the letters ABCD} onto {transformations of the square}.

The…

Dec 9th
3 notes

8 tags

Dec 8th

8 tags

Group Theory
Group theory supposedly belongs to “higher mathematics” but it’s more like a preschooler playing with coloured blocks than it is like abstruse journal articles full of pointy symbols.
Say you have a collection of things. And then you do stuff to them. Maybe there is only a finite range of options of what to do, as in

tying a knot

turning your mattress (apparently…

Dec 7th
5 notes

6 tags

Interstellar Dust
According to the movie Sunshine, most dust inside a house is old human skin.

What is “dust” in outer space made out of?

Dec 7th

5 tags

Dec 6th
9 notes

Seriously, though. What’s so great about Swiss Army knives?
Dec 5th
1 note

2 tags

Logical Circular Logic
Are the Israelis bellicose because countries are always antagonizing them, or are countries always antagonizing the Israelis because they’re bellicose?
Do you think that boy is cute because he likes you, and he likes you more because you like him, and where did this liking start in the first place?
If the rich get richer, how do you get rich in the first place? And if poverty leads to…
Dec 4th
5 notes

5 tags

Dec 3rd
7 notes

Dec 3rd
51 notes

6 tags

Sci Fi Now
People over-estimate what can be done in the short term, but under-estimate what can be done in the long term.
Weight loss is a perfect example. People think they can get in shape in a couple weeks before going to the beach (hard to do). But they don’t realize how much weight they could lose over a year by eating just 100 calories under their daily metabolic usage (answer: 10 pounds per…
Dec 2nd
3 notes

5 tags

Gas Clouds
Why don’t gas clouds in outer space collapse from gravity?

magnetic repulsion
rotation (centrifugal force)
turbulence

Dec 1st
4 notes

November 2010

43 posts

8 tags

Spacetime is Curved
“General relativity can be summed up in two statements:

Spacetime is a curved pseudo-Riemannian manifold with a metric of signature .
The relationship between matter and the curvature of spacetime is contained in the equation .”

—Sean Carroll

There you have it, ladies and gentlemen! The universe summed up in two sentences.
Regarding the first statement: a metric of…

Nov 30th
7 notes

6 tags

Nov 30th
4 notes

3 tags

Maybe Calculus Isn’t Bullsh*t
I may have to take back what I wrote earlier. I need to find out more about the Radon-Nikodym concept of a derivative.
Nov 29th
4 notes

3 tags

Weather
Predict the weather for the coming week by looking at the whole continent. If the jetstream is above you, you’ll get warm Mexican air. If the jetstream is below you, you’ll get cool Canadian air.
(Works if you live in the midwest. Of the US.)
Current National

Current Visible Satellite

Current Infrared Satellite

Current Temperatures

Current Northeast Temperatures

Nov 29th
1 note

“The good Christian should beware of mathematicians and all those who make empty…”

– St Augustine

Nov 28th
10 notes

7 tags

Nov 27th
1 note

3 tags

ListenThis new Andrew Bird jam makes me excited about…
Nov 27th
5 notes

6 tags

“In a space of high dimensionality, most of the volume of a cube is concentrated…”

– Neural Networks for Pattern Recognition by Chris Bishop
Problems 1.18, 1.19, 1.20
Machine Learning and Pattern Recognition by Chris Bishop

Nov 26th
1 note

Would You Be Happier If You Were Richer? →
The best determinant of someone’s level of happiness is how often they eat meals with friends and family.
Nov 25th
6 notes

5 tags

6-dimensional Sphere
Of course a 3-dimensional thing is bigger than a 2-dimensional thing. Just like a beach ball is bigger than a circle cut from paper. And it’s equally obvious that a 4-dimensional thing would be bigger than a 3-dimensional thing.

Or … is anything obvious? Following is a lesson in multi-dimensional reasoning.
A 2-dimensional “ball” is a circle. Two-dimensional points…

Nov 24th
8 notes

3 tags

Science. →
¡ You love it !
Nov 23rd
3 notes

10 tags

Math Infinity
Conceiving of ∞ as a mathematician is simple. You start counting, and don’t stop.
That’s all.
($i++ for programmers)
Which is why ∞ seems very small to the mind of a mathematician.
With projective geometry you can map ℝ to a circle, in which case there is a point-sized hole at the top where you can put ∞ (or −∞, or both).
Same thing with the Riemann Sphere.

So to them ∞ is…

Nov 23rd
12 notes

13 tags

Religious Infinity
When I was a lad, I used to — as an exercise — try to conceive of ∞. We would hear in Sunday School that God is Infinite, that you can’t comprehend God’s Infinite-ness.
I would imagine myself in a spaceship flying out to the edge of the universe. I would imagine all of the stuff we had left behind us, flying at the speed of imagination.
Then I would zoom out the camera,…
Nov 22nd
10 notes

6 tags

Nov 21st
35 notes

13 tags

The Speed of Imagination
When I was little, I asked my mom what was faster than the speed of light. I think my friend’s dad had been watching Star Trek while I was over and they talked about warp speeds on the show.
My mom said that the fastest speed is the speed of imagination. (Good answer, ma.)
So this was my understanding of universal speed limits when I was 10:

I also tried to incorporate Warp Speeds into…

Nov 20th
6 notes

5 tags

ListenConcave Growth Function
This is for my homies…
Nov 20th
2 notes

Nov 20th
1 note

7 tags

Public Debt the World Over →
Nov 19th
2 notes

6 tags

√π sqrt[pi]
π of course is the distance around a circle. √π is the area under ∫exp (−x²), and ∫exp (−x²) is the key ingredient in the normal distribution.

That’s more or less what √π means—the area under the Bell curve.
But what does it mean mean? I mean, if π is a distance and √ is used to turn areas into distances — is it, like, shrinking the π even one more time? Are we talking about…

Nov 18th
28 notes

9 tags

“[A] strong case can be made for the [random walk hypothesis]… This market…”

– Agustin Silvani, Beat the Forex Dealer

What I’m hearing—not for the first time by a trader writing a book—is the implication that the way to consistently make money as a trader is to make the market more efficient, more stable.
If I were running a company based on this asset, I…

Nov 18th
3 notes

4 tags

“The [foreign exchange] market is by far the largest and most liquid market in…”

– Agustin Silvani, Beat the Forex Dealer

Nov 16th
3 notes

Nov 15th

15 tags

Mindfulness
Think about this: those Eastern philosophies that are so helpful to modern Americans, ideas we use to disconnect us from our Blackberries, were developed by people with no electronic technology.
What does that mean? My picture of medieval anywhere (Asia, Europe, Africa) is peasants busting their backs in muck all day. At night a fiddler plays The Devil Went Down to Georgia and they all get down,…
Nov 14th
3 notes

1 tag

Nov 13th