All modern research questions frame your mindset and self-frame research paradigm. Broad thinking: how little of everything can a citizen survive on; how cheap can your upkeep be? /1

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Get a cup of coffee.

In this thread, I'll help you understand the basics of Binomial Thinking.

The future is always uncertain. There are many different ways it can unfold -- some more likely than others. Binomial thinking helps us embrace this view.

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The S&P 500 index is at ~3768 today.

Suppose we want to predict where it will be 10 years from now.

Historically, we know that this index has returned ~10% per year.

If we simply extrapolate this, we get an estimate of ~9773 for the index 10 years from now:

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What we just did is called a "point estimate" -- a prediction about the future that's a single number (9773).

But of course, we know the future is uncertain. It's impossible to predict it so precisely.

So, there's a sense of *false precision* in point estimates like this.

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To emphasize the uncertainty inherent in such predictions, a better approach is to predict a *range* of values rather than a single number.

For example, we may say the index will return somewhere in the *range* of 8% to 12% (instead of a fixed 10%) per year.

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10 years from now, this implies an index value in the *range* [8135, 11703]:

A Thread about Famous Armenian Inventors and what we have contributed to the world. So the next time someone wants to say we are unimportant, you can rest easy knowing Armenians have contributed some of the greatest inventions to mankind. Here is a handful but there's more.

Raymond Damadian: Armenian-American Physician and inventor of the first MRI machine. MRI is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. Raymond created the first MRI in 1977.

Artem Mikoyan: One of the most famous engineers in aviation. Mikoyan along with Gurevich created one of the most famous Jet lines in history, the MiG. MiG jets directly competed with American Lockheed Martin F Series planes and were among the first to surpass the speed of sound.

Hovannes Adamian: Most notably laid the foundations of color television with his Tri-Color Principle. His work would go on to become the framework that is used to create Color-TV that we see today. He is recognized as one of the founders of color television.

Emik Avakian: An inventor who unfortunately was disabled, but that didn't stop him from contributing work that would help people similar to his condition. Notable contributions are the automatic wheelchair which dismiss the action of hand rolling and a breath operated typewriter.

Wonder why your Ph.D./Master's application is being rejected?

Here are some insider reasons (from a committee member) that result in such "Love Letters" 👇

- A Short Thread

1) First, you should know that sometimes, an independent reviewer is required (especially in the US) to review applications even after PIs must have selected their candidates. So, even if any bias slips through the PI, the independent reviewer will pick it up.

2) Having said this, there are three major issues that application reviewers/committees often find with your application. These three components make your applications almost challenging to assess.

3) NUMBER ONE - Incomplete Applications

This occurs when you do not upload the requested documents needed to evaluate your file. Think of a candidate that did not send a GRE score when the institution clearly requires it for admission.

4) NUMBER TWO - Error laden Essays

This is particularly interesting because based on reports from this resource person, it is not particularly about how little your experience is but how you communicate it error-free or at least extensively minimized. This gives headache!

Best visual demonstration of God’s source code in action