"You don't see radio changing gradually and suddenly become radar. #Darwin's theory doesn't work for #technology, and we have to make a new observation."

- W Brian Arthur at SFI today

#evolution #innovation #invention

Did you know that all the nuclear bombs we exploded in the '40s-50s-60s have permanently contaminated all the steel the world has produced since then? All steel in the world is divided into two categories: pre-1945 non-contaminated steel, and post-1945 contaminated steel.

How?

Nuclear bombs (including the tests) create a lot of radioisotopes that are not found in nature. For example Cobalt-60 (a radioactive version of Cobalt-59). And since the 1945 Trinity test, these have all dispersed in the atmosphere.

What does this have to do with steel?

The process of manufacturing steel uses atmospheric air (or atmospheric oxygen). Some of the radioisotopes like Cobalt-60 get pulled in too, and as a result, any steel produced after 1945 has embedded in it some of these radioisotopes, sitting there emitting gamma rays.

Why do we care about traces of radioisotopes in steel? When making Geiger counters, or medical devices to check for radioactive contamination, or astronomical instruments, the emissions from the contaminated steel would interfere with the measurements.

So we need pre-1945 steel

Pre-1945 non-contaminated steel is called "low background steel". And when we need it, where do we get it from?

We go, find pre-World-War-II sunken shipwrecks, and then salvage the steel (and lead) from those to build our instruments which need heavy radiation shielding.

Some 1300 years ago in Karnataka there lived a genius who wrote "Gaṇitasārasan̄graha" (which is earliest text devoted entirely to mathematics)

The man who's work later borrowed by Arabs & Europeans

Thread on "Mahāvīracharya" astounding but forgotten legacy

Mahāvirachārya was patronised by rashtrakuta king amoghavarasha

His book"Gaṇita-sāra-saṅgraha"is earliest text devoted entirely to Mathematics

He has described the currently used method of calculating(LCM)of given numbers.The same method was used in Europe later in1500CE

Mahavira wrote "Gaṇita-sāra-saṅgraha" (GSS) in 8th century CE which contains some 1100 slokās & contains elementary topics in arithmetic , algebra , geometry , measurements , logic , number theory , dynamical systems etc

A sheer mathematical genius

He was devout jain
His magnum opus "Ganit sara sangraha " start with a sloka bowing to the glory of the jinas

"संख्याज्ञानप्रदिपेन जैनेंद्रन महत्वेशा,
प्रकाशितम जगतसर्व येन तम प्रणमाम्यहम"

He also praised his predecessor aryabhata , brahmagupta & other greats in his works

The importance & popularity of "Gaṇita-sāra-saṅgraha"was so huge that it enjoyed statues of most important textbook of mathematics in South Indian for over 3 centuries

A large no of manuscript copies of
"Gaṇita-sāra-saṅgraha"whr discovered in Kerala shows it's popularity

1/

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.

2/

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:

3/

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.

4/

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.

5/

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