Oil – Looking Down the Barrel?

Creative Destruction

I remember the opening line of the book “The Third Wave” by Alvin Tofler, the futurist:
A new civilization is emerging in our lives and blind men everywhere are trying to suppress it.

He wrote the book many years ago, but that sentiment is still true. Blind men cling to the idea that buggy whips will always be needed, that we must continue to mine coal  in order to achieve energy independence. But the handwriting is on the wall – the world is rapidly embracing a new paradigm which will spur a multi-trillion dollar change in direction. If we see it coming before the blind men we can get in early as investors, entrepreneurs and citizens.

In an oft-quoted comment Wayne Gretzky, the superstar hockey player, said, “I skate to where the puck is going to be, not where it is.” That was the rare ability that made him such a dominant player. It is the same in investing and entrepreneurship. Those that are successful don’t just look at the existing landscape, they see future trends and paradigm shifts and creative destruction and new worlds emerging from the destruction. They see the phoenix dives into fire and rebirths. They see Vishnu, the Destroyer of Worlds, and Brahma, the Creator of new Worlds!

Optimum – A 5 -10 Year Investing Horizon

Of course how far you can see into the future has limits. For a comfortable and practical investing horizon lets take 5 – 10 years. This, I believe, is the optimum time for trying to predict the economic puck’s location. Also, as a side note, I think that if you want to invest in the stock market you must have a buy and hold mentality of 5-10 years. In-and-out strategies are guaranteed to lose money because you’re playing in a  rigged game against professional players armed with large data, analytics, special information and nano-second trading. It’s like a game of poker where they can see your hand but you can’t see theirs! The largest professional short-term traders make a very large percent of the Wall Street profit, and the counter-parties to these profits are losers in the zero-sum game, usually small investors, day traders, large pools of managed money and the like. A 5-10 year horizon, however, is not where the sharks are feeding and you have an excellent chance.

[In fact, a purely passive strategy of buying a large cap US index fund with low fees, like the DIA (the Dow Jones Index Fund), will provide you with great returns over a 5-10 year horizon. You will probably beat inflation by 5 – 7% and you will beat 95% of the Mutual Funds! All this without lifting a finger. I keep repeating this in my blogs and for most investors this may be all the advice they need.]

But suppose you have insights about the puck as it is likely to be in 5-10 years. You can make better investment decisions. The trends for this time frame are beginning to become apparent but are not yet fully appreciated or widely acted on, making them an opportunity.

Death Watch

In the 5-10 year time frame the following large sectors should be on a Death Watch list

  • Oil, Coal, Gas – Fossil Fuels
  • Banks, Brokerages, Investment Houses, Financial Institutions.
  • Insurance Industry including Healthcare Insurance providers

These industries (and others) are in the early throes of an extinction spiral – not yet apparent to everyone. In 5 years it will be apparent to a lot of people but we want to act now before everyone bails.

In this blog let’s focus on the Oil, Gas and Fossil Fuels industry. We can hopefully take on the others in future blogs. Stay tuned.

Grim Reaper

To the blind men it looks like the oil and coal industries are essential to the world’s energy needs and will remain a part of a balanced investment portfolio. The US Energy Information Administration (EIA), which  makes official forecasts several decades out says in its 2016 report that in the year 2040 petroleum and other fossil fuels will still constitute 78% of the world’s energy use.

Here is their Summary:

“Even though consumption of nonfossil fuels is expected to grow faster than consumption of fossil fuels, fossil fuels still account for 78% of energy use in 2040. Liquid fuels—mostly petroleum-based—remain the largest source of world energy consumption, the liquids share of world marketed energy consumption will go from 33% in 2012 to 30% in 2040.  Coal, the world’s slowest-growing energy source, rises by 0.6%/year.

Solar will be the fastest growing at 9% per year, but still not enough to change the landscape much by 2040.”

This is so bad a prediction that it should qualify for malpractice in forecasting! Talk about the blind men! Solar is already producing more in 2017 than they predicted for 2020. In fact if you look at an internet article on solar predictions that is 6 months old it already feels woefully obsolete. Wikipedia predicted in mid 2016 that India will have 6 GW of solar by year end. The real number on Dec. 31, 2016 was more than 9 GW.

In fact solar will grow more than 25% per year! It will generate twice more energy in 2025 than the EIA predicts for 2040. The contribution from oil and coal will dive precipitously, down to virtually buggy whip levels.

Take this report, much more on the button from the insiders in the field. It says:

Cumulative solar PV capacity will double every 24 months. Since the inception of solar, there has been a total of 320 GWp built. Within the next two years, this total capacity will be doubled. In the next 4 years there will be 4 times as many solar installations.

Therefore, in 2018, there will be ~640 GW of PV installed and the industry will need to employ up to 5 million people. By 2020, there will be ~1,280 GW installed and possibly 10 million people employed.

At the same time, costs of PV panels will continue to drop, so PV electricity will be cost competitively in more and more local markets.

Here’s a visual cue to the future of energy as the deeper predictors see it. Green means significant or growing, Yellow stagnant and Red declining.

Energy Outlook

The oil industry (or the fossil fuel industry more generally) has a lot of champions, including the blind men in our current government. They are building a huge wall. Its  cost is trillions of dollars, not just billions. And you, not Mexico, will pay for it!

The Wall

wall of liesThe big wall that the oil/coal industry has built is one designed to keep facts out, bottled behind the wall. But for how long? Very soon the facts will build up, form an inexorable force and break the wall.

Here the the inconvenient facts that are blocked by this wall:

  • Global Warming is real. It is exacerbated by human fossil fuel burning and is not just part of the natural earth cycle. Moreover it can and will be economically addressed, creating new businesses and meaningful jobs. The whole world is on board with this. In the US there is deliberate disinformation being spread using enormous sums of money from entrenched fossil fuel interests and feckless politicians
  • There is also huge non-carbon pollution from the burning of oil and coal. It’s choking the air with toxic particles, pumping mercury and other pollutants into rivers, causing aquifer degradation and methane etc from fracking. (In New Delhi, India, for example where I was last winter, the air is unbreathable. Lung cancers are growing. Children are developmentally arrested. All from oil-burning cars and coal-burning plants nearby).
  • Oil has gigantic, civilization-destroying geo-political costs. Oil is the lifeblood that feeds the tumor of terrorism and causes us to engage with dreadful countries like Russia, Venezuela, Iraq and Saudi Arabia. If you really want to win the war on terror no need to “bomb the shit” out of the Middle East. Just get off oil.
  • Fossil fuels are no longer the economical solution for the world’s energy needs and a growing, thriving world economy. We don’t need to trade off growth and material well being against poisoning ourselves or being beholden to Russia and Saudi Arabia. This is because we have, for the first time, very viable and less expensive green options.

Of all of the above facts the one that will be most decisive is the last.

Solar is on Moore’s Law Journey

Already alternative green tech like solar is at parity with oil at $50/barrel in much of the world. This is true even when we do not recognize the true cost of fossil fuels by subsidizing them, not attributing CO2 costs to them, or terrorism-fighting losses to them. But solar power, in particular, is seeing an exponential reduction in cost. In ten years (or sooner) it will beat oil even at $10/barrel. And a big enabler of this green, plentiful and inexhaustible energy source is batteries. Great strides are being taken in solving the battery road block and soon solar will ride the Moore’s Law exponential curve. It is in the early stages of this exponential ride which could go on for decades. See my article on why Tesla, at the vanguard of the battery business,  will be a trillion-dollar company in 10 years.

The consensus among the energy industry Gretzkys, those who see the puck 5-10 years from now, is that we will leave up to 80% of all our oil and coal in the ground. This makes a lot of sense in bending the carbon curve while building a new economy with good jobsThink about it: we should value much of the oil reserves of oil companies at zero! I’m sure this sounds extreme but this is emergent reality.

I’m not including any Black Swan events in this prognostication which can further speed us into an alternative energy future. Black Swan events are by nature unpredictable so I don’t know what they’ll be. It’s still fun to speculate. Could it be a new revolutionary battery? Artificial photosynthesis? Genetically modified bacteria? Graphene-based semi-conductors?

We know with much forecasting certainty that the fossil fuel industry is headed to the gallows.

The oil stocks are already beginning to reflect a persistent malaise. For sure our current administration is going to fight this trend. They will deny all mention of CO2 harm, they will eliminate environmental protections, they will cut funding for green energy research and  subsidies. Even more, I predict they will try to sell off federal lands to oil interests in fire-sales, with subsidized mineral rights to big oil and coal interests. None of this will work for long. Reality is a formidable opponent.

A couple of weeks ago (on March 19th, 2017)  Dr. Ernest Moniz, the Energy Secretary under Obama was on Fareed Zakaria’s excellent CNN program, The Global Public Square, or GPS. He said that the Paris Accords were not just an agreement among countries to limit their emissions to specified levels. The main outcome of the Accords was a commitment to building shared new technologies and products toward a renewable energy future. Technologies such as new kinds of batteries, new integration of solar panels into building materials, new standards to allow uniformity and compatibility of products, improvements in Balance of Systems for solar. Also, offshore coastal grids for transmitting wind and solar power from ocean sites, and a host of other engineering innovations.

This will spawn a spate of new, well-paying and meaningful jobs. In manufacturing, construction, management, accounting, scientific research and even new art and literary expression. If the US signs out of this we cease to be a prominent player in this multi-trillion dollar emerging sector. The leadership will go to China, Germany, India and other committed countries. And our jobs will migrate out no matter how much global trade we ban.

From this perspective it makes little sense to invest in the fossil fuel industry. Losers will include large oil conglomerates, oil services companies, pipelines, coal interests and even the fracking and natural gas companies. It is interesting that pipeline partnerships such as Energy Transfer Partners have fallen in price despite support from the Trump administration and even when oil had a (dead cat) bounce. Dear TransCanada – sorry, the Keystone pipeline is not going to be killed by environmental concerns alone, you will be dead because we don’t need another 800,000 barrels of oil per day.

How to Invest

What is the best way to invest with a 5-10 year horizon? The passive purchase of the Dow Index Fund (DIA) or equivalent S&P 500 ETF remains the best approach for most. I know that the Dow 30 stocks have Oil/Gas, Financials, Brokerages as components. Still the 30 stocks are selected and monitored by very smart people  and they will most likely get out of dying sectors before the inevitable.

If one has a stomach to be somewhat more proactive, I would create my own large cap “Modified Dow”. It  would consist of all Dow stocks except  ExxonMobil, Chevron, Goldman Sachs, JP Morgan Chase, Travelers and American Express. I  would add in Tesla, some other tech stocks,   like Amazon, Google (Alphabet), even  Salesforce,  and some tobacco including a couple of international  giants, like British Tobacco. Throw in a progressive utility or two like Duke (active in green energy).  Also Tencent (SEHK) – a Chinese company that just bought a 5% stake in Tesla. The Chinese see the value of clean energy that is why they are requiring that companies that want to sell electric cars in China hand over their battery technologies! I hope we don’t give away our tech edge – now that would really be a bad trade deal.

I would buy equal number of shares of all on my list and not touch this for many years. Reinvest dividends.

This is not really an investment advice column. I’m stating a macro level view and guessing where the puck will be in about a decade. It’s purely a sharing of a personal perspective.

Posted in Current Events, Education, Innovation, Investing, Money, Philosophy, Politics, Science | 5 Comments

Tesla – The 25-bagger!


Screen Shot 2017-03-07 at 10.57.56 PMTesla looks so overpriced by all the usual metrics. It made a loss in the 4th quarter of 2016. Its revenues in the last year were about 7 billion and it is selling at a market cap of $40 billion. The stock has been flat for three years and they made that expensive purchase of Solar City. Elon has recently missed many deadlines  and the roll out of the $35,000 model looks delayed and money-losing.

And yet Tesla is very likely to be a 25-bagger in a decade. To be a 25-bagger it would need a market cap of $1 trillion, more than any other company in the world today, including the high-flying Apple, which is capped at $700 billion. It will sell for 25 times its current stock price of $250/share in a decade. Maybe sooner, Yup. And then it’ll probably triple from there in another few years.

To understand my logic consider these facts:

We live in a winner-take-all economy.

Winner-take-all  has always been the tendency in a free market system, but there is a lot of evidence that it is accelerating. In a March 3rd article in the Wall Street Journal  Jason Zweig says that winners are taking it all and it’s time to buy the winners.

Some examples:

. Google dominates the ‘search’ category despite major attempts by competition, like $10 billion spent by BING from Microsoft. Google 75%, BING 15%

. Amazon and Alibaba have destroyed their competition. In India, Flipkart and Snapdeal once considered on-line retail faves have begun biting the dust.

. Uber is valued at $50 billion plus. Next one in this category is Lyft with one-tenth the valuation.

. Apple is the dominant winner in the smart phone business – they got more than 90% of all of the industry’s profits since 2015.

. Facebook is gobbling up the “Attention Space” online with more than a billion users and an exponentially increasing database of user information that it exclusively owns. This monopoly gives it a huge advantage over everybody else in this category.

Other winners include Netflix, Adobe, Google’s You Tube in the video space (5 billion video viewings per day!). This market dominance is not just a feature of high tech – although it is faster and more obvious there. Banks and investment firms, like J. P. Morgan Chase, Bank of America, and Goldman Sachs, are once again concentrating in size and scope – the largest few being behemoths, too large to fail by any account. In Real Estate, Tobacco, Supermarkets and the Insurance sectors the same trends are very prominent.

In their recent book, Play Bigger, How Pirates, Dreamers, and Innovators Create and Dominate Markets,  Ramadan, Peterson, Lockheed and Maney point out that 54% of all profits in the last 5 years have gone to the category-leading companies. In the last decade start-up valuations have tripled, they found. But the rising tide doesn’t lift all boats any more. The Category killers got all the action – a six-year start-up that wasn’t yet “King” had an almost zero chance.

The reasons are manyfold. Today the advantages of being large greatly tilt the odds in your favor. In high tech the largest companies get the best talent, attract the largest number of  Apps from developers, have the best access to capital and get the biggest free buzz. Companies like Apple, Google and Amazon have a huge gravitational pull across the globe that sucks everything into their category space. Also they have the largest flexibility in growing their categories as well as defining new categories that they can naturally dominate.

So this throws out the wisdom of mere valuation as an investment criteria. Recently I had lunch with my friends, Steve Butler of Pension Dynamics and Blair Hull of Hull Investments, (Blair runs an ETF called Hull Tactical US) and we were discussing this very issue. Steve said that small-cap companies outperform the Dow companies over the long run. Small-cap returns historically, he said, are 12% annually vs 10% for the Dow. I think this is a fallacy going forward. In a winner-take-all market small companies have structural and competitive disadvantages that increase their risk of simply perishing unless they can dominate their category.

How should you invest in such an environment?

One timeless advice which requires minimal effort is to invest in a large cap index, such as the Dow Jones Industrial Average (DJIA) tracking DIA or the S&P 500 Index. The 30 stocks in the Dow tend to be dominant in their category – they represent 30% of the entire  market cap of all stocks- and thus have a lot to gain by the advantage that accrues to size. The DJIA has a well-documented 120-year record and has grown 10% compounded for this period, despite the 1929 depression, the dot-com bubble and the 2008 financial collapse. That means that you could double your money approximately every 7 years, beat inflation by a whopping 7% per year, and beat the US GDP growth rate by 3% or more per year! All with near-zero effort.

But you can do better if you can explicitly play the winner-take-all paradigm.
You can do this if you can spot an emerging category with a huge potential market size and then identify the company or players that will dominate it. This will be the potential winner-take-all and if you spot this company early before everyone else jumps in you have a market King with big returns. Many such players are not public yet so the biggest opportunities might lie in the Venture space. This is a hazardous space, not for everyone and not easy to spot the winners.

But there are areas where you might be able to pick up a publicly traded company that meets the above criteria. If you can spot such a company you have a potentially very rewarding investment – a multiple bagger. Tesla is one such dominant company in an exploding market.

Why Tesla?

So back to Tesla.  What space do they dominate – no, it isn’t electric cars. The big, emergent, giant category they dominate is Batteries. Batteries for home storage, solar/wind power generation, peak shifting by utilities and another million uses that will emerge as the price drops. And emergent is the word for this market.

Since mid-2016 Tesla makes their Powerpack (for utilities and industry) and Powerwall (for the home solar market) battery storage units.The price has already come down  15%  to about $400 per KWH and they reportedly have $1 billion in outstanding orders for 2017! That’s triple the order rate in 2016. At current prices that means 2,500 MWH of battery storage. Tesla is a leader in this field and it looks very likely that they will break the $100/KWH price target first, at which the battery market goes crazy. This will almost certainly happen in 5 years (by 2022).

How crazy will the battery storage market be? Let’s estimate.

Solar power generation in the US  is about 1% of total today – it looks insignificant and below everybody’s energy radar, but it’s doubling every 30 months. It will follow Moore’s law of exponential growth as costs come down and efficiencies of scale kick in. In 5 years it will grow four fold. In 10 years 16 fold. Such is the nature of exponential growth.

In 2016 solar generation in the USA was already at 54 trillion-watt-hours (TWH) which is more than 1.35% of total electricity generation here (about 4,000 TWH). Each TWH is a billion KWH. With prices coming down rapidly solar installations are growing and will continue to grow at about a 35% compounded rate of growth. Thus in 5 years solar will be at over 200 TWH or 4% of US electric output and in ten years at 800TWH or 16%. Wind power will most likely grow more slowly but starts at 200 TWH, four times the amount of solar today.

Both solar and wind produce power intermittently and need batteries to even out the electric usage. If you assume that, as a minimum, one day’s worth of consumption should be stored in batteries, the demand for storage for solar and wind (in the US alone) comes out as follows, according to my conservative calculations:

2022: 180 GWH
2027: 4000 GWH

The cost for storage will drop approximately by 15% per year – so assume that these demands are realized only for  $100/KWH of storage cost, about 1/4th of today. That makes the market size for this segment of battery demand to be:

2022: $18 billion
2027: $400 billion.

Batteries for cars, peak-shifting and non-US markets are not included in the above estimate.
Tesla will dominate this market – having a huge first mover advantage. Even at 75% of the market they will sell $13 billion of batteries in 2022 growing to a whopping $300 billion in 2027! Their first mover advantage is huge: a giga-factory in Nevada that will most likely produce 150GWH of battery storage per year, according to Musk. They also are sewing up a virtual monopoly on utility-scale storage with well-engineered, modular and small-footprint units. Other players and better battery technology may emerge to compete, but the likelihood is that Tesla will absorb them into its own orbit, either through acquisitions or collaboration agreements.

Add to this car sales, rooftop solar and other ancillary products for Tesla and we can, conservatively, say that Tesla could have sales of over $500 billion in ten years. This sounds wildly optimistic, but Elon Musk is planning for it and can pull it off. A trillion dollar valuation – a 25-bagger – easy! A decade from now this market will still be growing, it will not have reached a maturity stage. The demand for storage will be immense indeed and will not peak for at least two or three decades. So Tesla should get “growing” company valuations.

There are risks, of course. But such good bets don’t often manifest themselves and frankly we are still ahead of widespread recognition of this market segment and its exponential growth. Winner-take-all thinking in investing is still a new realization and not factored in by many in the market.







Posted in Current Events, Innovation, Investing, Money, Politics, Science, Uncategorized | 13 Comments

The Faked Fury of Fiorina

Fake Fiorinous Fury at the Republican Debate

Fake Fiorinous Fury at the Republican Debate

At the recent Republican debate held at the Reagan library, I found it hard to swallow the phoniness.

A fake video followed by fake outrage! Carly Fiorina gave a diva performance. Clenched teeth, seething rage, talk of butchered babies, body parts sold to Frankenstein labs for blood money. The image was one of a coven of Planned Parenthood witches with baby blood dripping from their fangs sucking at the Obama-supplied teet of government money… a horrific culture of death and big government that Carly will squelch like a cockroach. Man, she is impressive, if you ignore the content and concentrate on just the atmospherics.

So what’s the truth? Are abortions in America a run away epidemic? Are organizations like Planned Parenthood, motivated by gain and a liberal (meaning immoral) mindset, adding to the epidemic?

Let’s take a  look at abortions in America.

The simple fact is that you reduce abortions by reducing unwanted pregnancies, specially among unmarried teens and underprivileged young women. Planned Parenthood and many other subsidized organizations spend a bulk of their effort in preventing unwanted pregnancies – through advice, free contraception and a presentation of options to young women. And how have they done?

Here’s a chart showing the U. S. abortion rate since 1980. (Data from Guttmacher Institute)

US Abortions per year

After 1990 the abortion rate has steadily come down from approximately 1.6 million abortions per year to about 1.0 million in 2012, which is the date where the latest figures are available (the red dot in the above diagram). It’s projected to be even lower today at less than 900,000. A large part of the gain has occurred under the Obama and Clinton administrations although the decline has been steady for 25 years. This data is from the Guttmacher Institute which collects detailed statistics on women’s health issues.

The decline is a direct result of reducing unwanted pregnancies – teenage pregnancies are down by 40% in the US in the last 7 years. That’s how you reduce abortions – not by criminalizing it, or taking away reproduction-based counseling  provided by organizations like Planned Parenthood.

What would be an ideal goal for America?
Zero abortions.

But not because it is illegal or difficult to have one.

Zero abortions, because abortion bloodwe have young women in charge of their lives, supported by community, counseled on their options, and completing their educations, instead of having to drop out to be single mothers. There are far too many young women in this country that face very difficult choices –  poverty, broken homes, alcoholism in the family, hopelessness and community indifference. For such women Planned Parenthood provides education, support and options such as contraception, adoption and unfortunately even abortions.

By insisting that we should shut down public resources for Planned Parenthood we will not achieve the goal of zero abortions, we will do the opposite.

So, Carly, what do you say – let’s double the support for organizations like Planned Parenthood and accelerate our journey to Zero Abortions?

Posted in Abortion, Planned Parenthood, Uncategorized | 1 Comment

Ready for Prime Time?

Prime numbers never cease to enthrall and fill us with wonder. There is something about them, I don’t know what, but if you catch the bug you will never stop being amazed. (Prime numbers are those that have no factors other than 1 or themselves, e. g. 7 or 13)

Take Mersenne numbers. They are named after the 17th century French monk who studied them and are of the form:  2^n – 1, or 2 raised to the power n for some positive integer n, minus 1. The first few are: 1, 3, 7, 15, 31, 63, 127, 255 …. Since 4 out of the above 7 (not counting the number 1, which is outside the realm of numbers eligible to be prime) are prime, Mersenne thought that this series would be a rich source of prime numbers. He conjectured that an infinite number of these numbers would be prime – something that may be true but hasn’t been proven yet.

But the Mersenne series does yield some interesting properties. First, the exponent of 2 (i. e. the power to which 2 must be raised in a Mersenne number) must itself be prime! And even then very few prime exponents actually result in a Mersenne prime. Even so, last year, the largest prime currently known to man. a Mersenne prime, was found using fast computer searching. It is the 48th Mersenne prime and has more than 17 million digits!

The largest prime known: 257,885,161 − 1, a Mersenne prime.

(If you can be the first to find a prime number with more than a hundred million digits I believe there is a prize of $150,000 awaiting you  – so go at it!)

Mersenne numbers are also an example of an area of mathematics called Dynamical Sequences. Here you generate numbers, starting with a seed, such as zero and repeatedly plugging into a simple algebraic expression. For example you can generate the Mersenne numbers by using the expression 2x+1. Start by plugging x=0 and the expression calculates out 1. Now plug 1 into the expression and you get 3. Repeat and you get 7 followed by 15, 31, 63, 127 …  i. e. the Mersenne numbers.

Holly Krieger, currently at MSRI* (see below) in Berkeley, is studying the arithmetic properties of some magical dynamical sequences and coming up with mind blowing results! MSRI has a video series at the website Numberphile.com full of fascinating math games, puzzles, tricks and number facts. To see a wonderful show on her dynamical sequences and how prime numbers crop up everywhere see her presentation by clicking her picture below. Do see it all the way to the end for she has an unexpected surprise!

*MSRI – Mathematical Sciences Research Institute, Berkeley. Website here. MSRI is an advanced institute located in the Berkeley hills dedicated to the advancement of fundamental math and also to the cultivation of its beauty, power and importance.

I have the privilege to support some of their activities and in return get a rich exposure to fun math people and cutting edge researchers in the field. Next time you’re in Berkeley check them out. Ashok

Posted in Cosmology, Education, Fun, Math, Philosophy, Puzzles, Science | 1 Comment

Six Cherished New Year’s Wishes

I’ve been thinking Math this last week. We had the Math Lover’s Forum at our house – a gathering of Math enthusiasts in an intimate setting discussing a problem of deep interest.

Prime Obsession

Prime Obsession

One of the attendees, Sean Hennessee,  brought along a book for me, Prime Obsession, by John Derbyshire. As it says on the subtitle of the book, it’s about: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics.

It’s amazing how much fun Math books like this can be – you really don’t even need to be a very deep scholar to love them, although it helps to be curious about the subject. I remember reading One, Two Three.. Infinity by George Gamow many years ago – a book that got me started loving all the math lore and magic.

Another fun book that I read many, many years ago is, A Mathematician’s Apology by G. H. Hardy, the celebrated Trinity College (Cambridge) don who discovered S. Ramanujan. He describes his own life as a mathematician elegantly and walks us through the corridors of Trinity College where the likes of Bertrand Russell, John Maynard Keynes, John Edensor Littlewood, James Clark Maxwell were doing world-changing science and where Ramanujan spent several years, a complete social misfit but a huge natural genius that everyone at Cambridge tried to adopt and understand.

There are many fun stories about Hardy and other prominent Mathematicians (Gauss, Euler etc.)  in Derbyshire’s book along with an exploration of their genius and passion for math. The “Unsolved Problem” that the book talks about is The Riemann Hypothesis,  one of 7 so called Millennial problems in Mathematics that has a $1,000,000 prize for its proof. It is the most talked about enigma that the math community incessantly talks of and is indeed a problem with a lot of astonishing twists and turns, all brought out very nicely in this book.

Here’s a fun story about G. H. Hardy from this book, which illustrates his interests and mindset. In a postcard to a friend around 1920 he talked about his six most cherished New Year’s Wishes:

1. Prove the Riemann Hypothesis.
2. Make 211 not out in the fourth innings of the last Test Match at the Oval in London.
3. Find an argument for the non-existence of God which shall conc=vince the general public
4. Be the first man at the top of Mt. Everest.
5. Be proclaimed the first president of the USSR, of Great Britain and Germany!
6. Murder Mussolini

Isn’t that a fantastic list! Wouldn’t you just love to chat with a genius who had that kind of New Year’s wish list?

What would be your six most cherished wishes?

In my next blog my New Year’s wishes (It’s New Year’s day tomorrow by the Hindu calendar. Happy Diwali and New Year’s everyone!). Also in a future blog another fun story from Hardy!

Posted in Cosmology, Education, Fun, Innovation, Math, Philosophy, Puzzles, Science | Leave a comment

Wolfram Alpha – A Wonderful Math Knowledge Engine

I was talking to my smart nephew the other day. He loves math and loves even more to stump me with math riddles and puzzles.

Me: Let’s talk about some fun problems with prime numbers*. I’m thinking of two prime numbers that add up to 753, what are they?

Nephew (instantly): Oh, come on, Uncle. That’s too easy. Clearly if the sum of two numbers is odd (in this case 753) then one of them must be even and the other odd. But the only even prime number is 2, so your numbers are 751 and 2.

Me: OK, you’re a genius.

Nephew: I have one for you. Think of prime numbers with a single digit repeated many times. The smallest such number is 11. What’s the next one?

Me: OK, Let’s see. A single digit repeated. A number like 777, hmm. Clearly the digit cannot be anything other than a 1 because if it’s any other digit like 7 the number will be divisible by 7 and hence not prime.

Nephew: Good

Me: So the prime will be composed of repeating 1’s. It’s not 111 because 111=37×3. It’s not 1111 because that can be divided by 11. What about 11,111? How do I check what the factors are for 11,111 or whether it’s a prime?

Nephew: You’re on the right track, my smart but oh-so-out-of-touch Uncle. Have you tried a great tool called Wolfram Alpha? It’s an Answer Engine as opposed to a mere search engine. It actually calculates your query using the famous computational program, Mathematica, written by scientist, Stephen Wolfram. Among other things it will factorize any number for you – within limits, of course. No one can factorize extremely large numbers, those containing say 100 digits, yet. But Wolfram Alpha will do any math that is possible, even including symbolic math and closed form equation solving,  and will give you the latest conjectures to boot.

Try it and see if you can factorize 11,111.

So I pulled up my iPad, went to the site www.wolframalpha.com and typed in “factorize 11,111” as below:

Wolfram Alpha Query

Back came the answer:

Screen Shot 2013-02-18 at 4.12.40 PM

It had factored my number: 11,111 = 41 × 271.

Me: You have shown me a great new resource, dear nephew. Now I shall try numbers with repeated 1’s to find a prime number.

Nephew: Great! And did you notice that you only need try numbers with 1’s repeated a prime number of times? So you needn’t try 1 repeated six times or 111,111 because 6 is composite. Since 6=3×2, you know 111,111 will be divisible by 11 or 111. Right?

Me: I was just going to say that myself. So the next numbers we will try will have repeating 1’s: 7, 11, 13, 17, 19, 23…. times. We tried them on the Wolfram Alpha Math Engine and got:

7:     1 111 111 = 239 × 4649
11:    11 111 111 111 = 21 649 × 513 239
13:    1 111 111 111 111 = 53 × 79 × 4187 × 265 371 653 × 14 064 697 609
17:    11 111 111 111 111 111 = 2 071 723 × 5 363 222 357
19:    1 111 111 111 111 111 111 = Prime!!!

Success! The smallest prime number with a repeating digit (after 11) is 1,111,111,111,111,111,111 or 1 repeated 19 times! We would never have been able to compute this using any conventional program like Excel or a traditional search!

Turns out the next one is 1 repeated 23 times and then we don’t see any more primes of this form for quite a while. They are there though. Many have been found but it’s a tough job even for very fast supercomputers.

Wolfram Alhpa is a real boon. Try it if you love playing with numbers or symbolic math. Here’s one last result I got playing with this fantastic math engine. I asked for the integral of secant(x). The answer, along with graphs, a Taylor’s series expansion and much more came out as below:

Screen Shot 2013-02-18 at 4.37.01 PM

What a fun resource available to all math freaks!

*(Prime numbers, as most of you know are numbers that cannot be divided by any other number, except of course 1. Examples are: 2, 7, 11 but not 21 because that can be divided by 3 and 7).
Posted in Education, Fun, Innovation, Math, Puzzles, Science, Uncategorized | Tagged | 7 Comments

“Goodness Gracious Me!” – A Classic from 1960

Millionairess PosterPeter Sellers has done some wonderful roles in his life time. In 1960 he starred in the movie “The Millionairess” with Sophia Loren. It is a hilarious comedy in which Peter Sellers is an Indian doctor living in London and Sophia Loren is his millionairess patient. She has fallen in love with him and feigns all kinds of illnesses to come and see him.

There is a great song from this movie called “Goodness Gracious Me!” which was a hit, particularly in India. It has hilarious lyrics, e.g.

Sellers loren millionairessFrom New Delhi to Darjeeling
I have done my share of healing,
And I’ve never yet been beaten or outboxed,
I remember that with one jab
Of my needle in the Punjab
How I cleared up beriberi
And the dreaded dysentery,
But your complaint has got me really foxed.

When I was a teenager in New Delhi this song used to play on the radio a lot and hearing it again it brought back big memories and I laughed hard once again as I did in those magnificent 1960’s and my college days. How fondly I remember them!

I’m appending a YouTube rendering of this song below. Please watch and you will love it. Also rent the movie, The Millionairess if you can find it. It’s a lot of fun.

Some things are evergreen!

Posted in Fun, Old Movies, Travel, Vacation | Tagged , | 6 Comments