Herstory of money-1 | 钱的历史

This is the first installment of a series of post about money, cryptocurrency and credit scoring, accompanied by Python Jupyter Notebook in our GitHub repo on credit scoring.

In this post we talk about paper money 纸币.  The reason why we keep it in the practical math category is because the herstory of money is also the herstory of math.  In God we trust and in math we trust.  God made the universe with beautiful math.

Did you know that paper money 纸币 was first used in ancient China around the 11th century 北宋朝?

Paper money was used broadly during those days due to shortage of copper and the convenience of paper money. However, the convenience combined with the unlimited power of the government to print money lead to inflation, subsequently the loss of credibility of the government, and its eventual downfall. So, even though the Northern Song dynasty had an advance monetary system, its credit failed due to long and costly wars.

Did you know that the Chinese Southern Song 南宋 dynasty government printed money in no less than six ink colors to prevent counterfeiting?

They printed notes with intricate designs and sometimes even with mixture of unique fiber in the paper to avoid counterfeiting. That was in 1107!

Backed by gold or silver too?

Isn’t it amazing that their nationwide standard currency of paper money was backed by gold or silver?! That was in between 1265 and 1274.

In the 13th century, Chinese paper money of Mongol Yuan 元 became known in Europe through the accounts of travelers, such as Marco Polo

“All these pieces of paper are, issued with as much solemnity and authority as if they were of pure gold or silver… with these pieces of paper, made as I have described, Kublai Khan causes all payments on his own account to be made; and he makes them to pass current universally over all his kingdoms and provinces and territories, and whithersoever his power and sovereignty extends… and indeed everybody takes them readily, for wheresoever a person may go throughout the Great Khan’s dominions he shall find these pieces of paper current, and shall be able to transact all sales and purchases of goods by means of them just as well as if they were coins of pure gold”
— Marco Polo, The Travels of Marco Polo

Saving Ipython script history

%save sessionName linesToKeep

This will save script in line numbers you specify in linesToKeep,for example, 1-20 34-50 64 into a file called “sessionName.py” in your current working directory.

If you are not so specific on which lines you want to keep, you can save everything.

%save sessionName ~0/

This saves everything from the current session, denoted as “~0″ into file “sessionName.py” in your cwd (current working directory).

%save pastSession ~1/

This saves everything from the past session, denoted as “~1” into file “pastSession.py” in your cwd.

scikit-learn processes simplified | 简化scikit-learn过程

Code light and concept heavy–that’s been the trend as programming languages stack on one another to wrap up more and more algorithms with fewer and fewer lines of code. A child can run a linear regression model. Yes, you hear it right. We have done it, and we summarize the building blocks of Python machine learning library scikit-learn in this table:

Process Code
Import libraries %matplotlib inline

import numpy as np

import pandas as pd

import matplotlib

import matplotlib.pyplot as plt

Format pd.options.display.float_format = ‘{:20,.3f}’.format
Import data from sklearn.datasets import load_boston

dataset = load_boston()

Prepare data y = dataset.target

X = dataset.data

Split data from sklearn.model_selection import train_test_split
Algorithm a from sklearn.linear_model import RidgeCV

my_regr = RidgeCV()

Train-predict my_regr.fit(X_train, y_train)

y_pred =my_regr.predict(X_test)

Plot – performance f, ax =plt.subplots(1, 1)

ax.scatter(y_test, y_pred)

plt.plot([0, 50], [0, 50], ‘–k’)

ax.set_ylabel(‘Target predicted’)

ax.set_xlabel(‘True Target’)

ax.set_title(‘Ridge regression on test data’)

ax.text(5, 40, r’$R^2$=%.2f, MAE=%.2f’ % (

   r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))

ax.set_xlim([0, 50])

ax.set_ylim([0, 50])

Interpretation interpretation = pd.DataFrame({‘X’: dataset.feature_names, ‘coef’: my_regr.coef_})
Algorithm b from sklearn.model_selection import cross_val_predict

from sklearn import linear_model

Train-predict my_regr = linear_model.LinearRegression()

y_pred = cross_val_predict(my_regr, X, y, cv=10)

Plot – performance f, ax =plt.subplots(1, 1)

ax.scatter(y, y_pred, edgecolors=(0, 0, 0))

plt.plot([0, 50], [0, 50], ‘–k’)

ax.set_ylabel(‘Target predicted’)

ax.set_xlabel(‘True Target’)

ax.set_title(‘linear regression with cross validation’)

ax.text(5, 45, r’$R^2$=%.2f, MAE=%.2f’ % (

   r2_score(y, y_pred), median_absolute_error(y, y_pred)))

Jupyter notebook markdown tips

Tip No. 1- Tip No. 100000: play around and click every button. If you are willing to do this continuously, you will be better than half of the programmers soon, and probably can answer most of the questions in Stackoverflow related to Jupyter Notebook markdown. Go ahead, it won’t break. The worst it could happen is restart. If you have to undo, hit Esc, then ctrl + z.

More

python numpy basics | 基础 python numpy 1

Tonight our class played together numpy basics and math.  We put together a numpy basics notebook:
https://nbviewer.jupyter.org/github/magicmathmandarin/PythonBasics/blob/master/numpy_basics1.ipynb#back-to-top

Programming by trial and error is a great way for kids to learn not only programming but also math. — this should play a bigger and bigger role in children’s day to day learning.  玩编程也帮助学习算术。

Somehow I have a feeling that learning long division in this day and age is wrong.  在这个时代还学长除法那就不对了。

Go ahead and tinker with the code in the notebook. Nothing will break, we promise 🙂

tensorflow upgrade and testing | tensorflow 升级和测试

It has been over a year since I last used tensorflow. Not only library versions have changed, but also the syntax. My old jupyter notebook was throwing errors all over the place this morning. It is time to update everything.

For tensorflow, I am using Python 3.6.3 (I used to use Python 3.5), and numpy 1.16.1. TensorFlow has a few dependencies. numpy is one of them. Note the mnist dataset has 70,000 images.

python -c ‘import tensorflow as tf; print(tf.__version__)

More

An great collection of Python notebooks | Python 笔记本集

Here is a really great collection of Python notebooks with lots and lots of links.  We start with some appetizers:

But there are so many and so much more!! Okay, I am just going to copy (fork) most of this page:

Mathematics

  • Linear algebra with Cython. A tutorial that styles the notebook differently to show that you can produce high-quality typography online with the Notebook. By Carl Vogel.
  • More

Women, men and money

From a dataset on restaurant tip included in the Python seaborn library, we investigate using Python with Jupyter Notebook how much money women and men relatively make, and why.

Most people don’t tip more or less because of server is a man or woman, but we do tip according to tip amount (for equal services).

I will tell you base on data analysis the real reason women make less is mostly because:
1. women work mostly lunch shifts
2. lunch bills are smaller than dinner ones.

Indeed, in every industry, including food services like in the restaurants, women have shouldered more share of the most difficult job in the world: parenting, and dedicated their time and energy to their families.

As a result, they have earned less money than men on average. Let’s give our appreciation to women for their roles in taking care of families!

There is a profound reason why we say “Mother nature”!

Should women work more dinner shifts and leave the important job of taking care of children to …?

That is a difficult question… Take a look at this Jupyter Notebook for the detailed data analysis.
More

Math olympia medal count analysis | 奥数奖牌分析

The International Mathematical Olympiad (IMO) is an annual six-problem mathematical olympiad for pre-college students younger than 20. The first IMO was held in Romania in 1959. As we will see, eastern Europeans were top performers in the IMO in the earlier years. You can find the summary data analysis in our Jupyter Notebook on GitHub.

It has since been held annually, except in 1980 (what happened in 1980?). More than 100 countries, representing over 90% of the world’s population, send teams of up to six students (under 20 years old) to compete.

Problems cover extremely difficult algebra, pre-calculus, and branches of mathematics not conventionally covered at school and often not at university level either, such as
– projective and complex geometry
– functional equations
– combinatorics
– number theory (where extensive knowledge of theorems is required).

No calculus is required. Supporters of not requiring calculus claim that this allows “more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity”.

Rank Country Appearance Gold Silver Bronze Honorable_Mentions
0 1 China 32 147 33 6 0
1 2 United States 43 119 111 29 1
2 3 Russia 26 92 52 12 0
3 4 Hungary 57 81 160 95 10
4 5 Soviet Union 29 77 67 45 0
5 6 Romania 58 75 141 100 4
6 7 South Korea 30 70 67 27 7
7 8 Vietnam 41 59 109 70 1
8 9 Bulgaria 58 53 111 107 10
9 10 Germany 40 49 98 75 11

Debt | 债务

Exactly two years ago, we wrote about national debt.  It was close to $20 trillion at that time.  Now it is $22 trillion.


We are  presenting  very large numbers.

But large is only a relative term, depending on the unit we are using, and relative to what.

According to the Institute of International Finance, global debt, as of 3Q2018, is close to $244 trillion.
About one third of the debt was added in the last ten years or so. So that means that over the last ten years the total global debt grew by a half.

You can see it from the Global Debt Monitor January 2019 Report.

This probably does not mean much to you or me, unless we have some comparisons.

Visuals can help you see the numbers, but it stops short of helping us to understand the number, since money in dollars is just money in dollars unless we compare it with something.

How about we compare it with GDP (gross domestic product)? GDP in dollar is the value of all the things people produce or service for a period of time in dollar.

So debt to GDP ratio is like the amount of money you owe at the end of the year relative to the amount of money you have made over the year.   When the ratio is over 1, it means what we owe is more than what we have made in a year.

Now hopefully we can understand the ratio a little bit.

For a great narrative of history of US debt to gdp ratio, see “The Long Story of U.S. Debt, From 1790 to 2011, in 1 Little Chart” from The Atlantic by Matt Phillips.

The article was written on Nov 13, 2012. But history does not go away.

You can connect the dots to the following chart, which you can find from Federal Reserve Bank of St. Louis.  It seems that we have debt to GDP ratio getting close to historical highest level.

That was right after World War II.

So what is in the US debt?

The total US debt now is about $22 trillion.

The U.S. debt to China is $1.138 trillion as of October 2018. That’s 29 percent of the $3.9 trillion in Treasury bills, notes, and bonds held by foreign countries.

The rest of the $22 trillion national debt is owned by either the American people or by the U.S. government itself. China has the greatest amount of U.S. debt held by a foreign country.

Domestically, the total US household debt as of 4Q2018 is at $13.54 trillion (New York Fed). For a fantastic and fascinating visual account of the numbers, see the report by New York Fed.

You can find the numbers and reports easily from different federal reserve banks and government office such as the Congressional Budget Office, and the US Treasury.

These numbers, ratios and time series by component are a lot more interesting and tell a whole lot more than everyday noisy news.