How long does it take to count to 1 million? 1 billion? 1 trillion?

Posted In: Math | Programming
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My son likes large numbers (like septillion, googol and googolplex) and once asked me how long it would take to count to septillion (which is 1 followed by 24 zeros).  I told him it would take longer than the age of the universe to do that, so he started working his way down.  He asked me about counting to one million.  I did a little math (assuming one number per second) and got about 11-12 days . . . but then thought, the large numbers (like 658,243) take more than a second to say.

Looked on the web a little to see if anyone else had done a more sophisticated calculation.  Lots of calculations were like my own (assuming one number per second).  Others acknowledge that it would take longer for large numbers and made assumptions about what that would be.  But nothing definitive, so I thought I’d make one.  This counting calculator is based on the number of syllables in every number and counts all the syllables you’d have to pronounce in order to count from one to one million (or other numbers).

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How Much Water is in California Reservoirs? – Current and Historical Visualization

Posted In: Water
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California has had an issue with drought, especially for the past few years now.  Recently, 2016’s El Nino weather pattern has brought a significant amount of rain to the state and helped alleviate some, but not all, of the major issues.  
I’ve been very curious to understand how the rain storms we experience are lessening the impact of the drought, and whether one wet season (like 2016) can really “get the state out of a drought”.  One way to assess this is to look at the status of California reservoirs.

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When Can I Retire? Early Retirement Calculator / FIRE Calculator

Posted In: Financial Independence | Money
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How long do I need to save before I can retire?

This early retirement calculator / visualizer is designed to project the number of years until you can retire, based upon a few key inputs such as annual income and spending, income growth rate, expected annual spending in retirement and asset allocation. It is a pre-retirement calculator that is useful before you retire to get a sense of how many years it is likely to take to accumulate enough money to retire. The three primary modes that are available in the early retirement calculator are: (1) constant, single fixed-percentage real return rates, (2) historical series of real returns are applied to account for likely variability in future returns and (3) monte carlo simulation of the variable returns based upon user-specified input parameters.
This interactive calculator was built to let you play with the inputs and help you understand how savings rate and retirement spending strongly determine how long it will take you to save up for retirement. Note: it does not simulate the post-retirement period when you start to draw down your savings.
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Post-Retirement Calculator: Will My Money Survive Early Retirement? Visualizing Longevity Risk

Posted In: Financial Independence | Money
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Rich, Broke or Dead?

You may notice that additional features have been added to the calculator (taxes, investment fees, and ability to add other income sources (e.g. social security) and other expenses to the calculator).
One of the key issues with retiring is the question of outliving your money. This is also known as Longevity Risk and is especially important if you want to retire early, since your retirement could be 50 years long (or more). This interactive post-retirement calculation and visualization looks at the question of whether your retirement savings can last long enough to support your retirement spending and combines it with average US life expectancy values to get a fuller picture of the likelihood of running out of money before you die.

It helps to answer the question: If I start out with $X dollars at the beginning of my retirement, will I run out of money before I die?

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Should You Invest (Or Wait) When The Stock Market Is At An All-Time-High?

Posted In: Financial Independence | Money
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The stock market has been on a bull run (hitting numerous all time highs) for the last 8+ years and it’s not clear when it will end. Whenever there’s been an extended bull run, one question that comes to mind “Should I invest in the market now, or wait until a pullback?” The question comes about because of fear and loss aversion: fear that the market will drop right after they invest and the observation that people want to avoid losses more than they value gains. However, historically, the correct answer, at least over the last 68 years, has been to invest and not to try to time the market.

This was also demonstrated in the Market Timing Game; that people are pretty bad at predicting the direction of the markets and given the upward trend of the market, it’s simpler and more likely than not, better to just stay invested in the market. The corollary to this is that when you have additional money to invest (e.g. from regular savings from your paycheck or a one-time event like the sale of a house), it makes sense to invest the money and not worry about whether the market is at a high or low point. Some graphs that look at the distribution of returns when the market is at an all time high (ATH) can help answer this question of whether you expect to see worse returns than investing at other times.
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Shall We Play A (Market Timing) Game?

Posted In: Financial Independence | Money
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The Market Timing Game simulation is premised on the idea that buying-and-holding index investing and index funds are a no-brainer investment strategy and market timing (i.e. trying to predict market direction and trading accordingly) is a less than optimal strategy. The saying goes “Time in the market not timing the market”. In this simulation, you are given a 3-year market period from sometime in history (between 1950 and 2018) or you can run in Monte Carlo mode (which picks randomly from daily returns in this period) and you start fully invested in the market and can trade out of (and into) the market if you feel like the market will fall (or rise). The goal is to see if you can beat the market index returns.
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¿Cuánto tardarías en contar hasta un millón?

Posted In: Counting | Fun | Math
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Disculpe(n) mi pobre español. Utilicé google translate para escribir esto en español.
Aquí está la calculadora que calculará cuánto tiempo lleva contar un millón (o números mayores) en español.
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Financial Freedom Calculator (Multi-Period FIRE Visualization)

Posted In: Financial Independence
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This is an update to the Financial Freedom Calculator. That one still works well, but this version adds the ability to add multiple savings amounts representing different periods in time. This allows you to visualize your progress towards financial freedom rather than just giving you the latest value for your freedom date. It does so by showing different colors for the different periods (you specify them by adding different savings amounts and names). It should be fairly obvious looking at the calculator, but if you had a total of 25000 in savings in 2016 and 70000 in 2017, then your calculator is colored in two sections representing the freedom days you had achieved in the two different years.
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