Pizzeria at the End of the World

There is a place known as the Pizzeria at the End of the World. They serve pizzas but who doesn’t? They have also installed some computer software to collect orders and to analyze the incoming data for all kinds of patterns and regularities which may occur. Just to be ready for every customer’s whim and for always changing trends and demands. It becomes a science, selling pizzas these days, but what doesn’t?

So, one night, after closing the shop, papa and mamma are driving home. “You know”, started the wife, “computer says, today, there were no two same orders, looking by kinds of pizza served to a table. Not two, despite the fact it was a lot of customers and a lot of pizzas sold!”

“Really?”,  says the husband. “Two orders are the same by pizza kinds, if and only if, for every kind of pizza on one order, there is this very same kind of pizza on the other order as well?”

“Yes.”, says the wife, her name was Martha, “One Margarita with two Hawaiian pizzas or two Margaritas with three Hawaiian pizzas are not equal orders, but they are equal by pizza kinds!”

“Very well”, says the husband, his name was Marco, “At least one of those two possible orders was not ordered today, right? And the salads and drinks are all ignored here, am I right?”

“You are always right!”, says Martha. “Moreover, the computer says, that for every pair of orders today, there was one order equal to those two orders combined! Equal by pizza kinds, that is!”

“What an amazing coincidence!”, says Marco. “This computer is too smart for his own good!”

“I wonder”, says Martha, “if there is a kind of pizza ordered today, present on the majority of all orders?”

“Ask the computer”, says Marco, “if there is an order with only one kind of pizza on it.”

“Computer says there is not. This might be good for our business.”, replied Martha.

Then the Wifi connection to the computer back at the Pizzeria at the End of the World, somehow disconnected. So Martha and Marco were on their own for a while.

He says: “You know dear, probably there was a pizza so popular today, that the majority of orders did contain it. I don’t know which one. Today’s state of the art mathematics isn’t powerful enough to ascertain that this is actually the case!”

“Yeah, I realize this now!”, says Martha. “We’ll wait until tomorrow to see. If there is and which one it is.”

Question. At least how many varieties or kinds of pizzas are served at the place, known as the Pizzeria at the End of the World? Assuming the computer, Martha, and Marco are all correct at everything they spoke.

It’s not a trick question, or a joke, or something of that kind. 

Solution is here:



COVID-19, A View To a Kill

The R0 factor for this illness, which denotes the average number of people infected by a carrier, isn’t a constant, it’s a function of time. R0 = R0 (time). In fact, it’s a function of more parameters and not just time. For example, if quarantined, R0 should be close to 0. There are many unknown factors here, of course, some even known. Some push this now well known R0 term bellow 1, others above 1. It’s all about reducing R0 below 1, and the illness will die out. Otherwise, the number of sick people will go through the roof, by the exponential growth function manner.

All of the above is very well known and understood and repeated over and over again now.

Then you get infected, you caught the virus somehow, what now? Your cells will spread the virus among each other by the factor R0IC !

R0IC is the average number of cells, one infected cell will further infect on average. “IC” in standing for “Inter-Cellular”. This is again not a constant but is a function of time and many other known and unknown factors. For example time, temperature, the immune system activity and so on. R0IC = R0IC (t, T, ISactivity, …, ). At least as complex as the transmission factor R0 between humans, is the transmission factor R0IC between cells. When R0 falls bellow 1 for a considerable time period, the epidemics burn out. When R0IC  falls bellow 1 for a considerable time period, the particular human’s illness burns out.

The last paragraph above is a less well-known fact, but it’s a fact none the less. Spreading of this virus among cells, in a way closely imitates the spreading among humans. Medical doctors and medical nurses work hard to minimize R0IC in already infected people. They might call it differently, but it is what it is. Stoping the intercellular infection, “flattening the curve” inside the patient’s body, “delaying the disease” inside the patient’s lungs — you name it!  Medical professionals thus “delay the disease” inside you, hoping that the immune system will kick in and do the same until done.

Now, when you are infected and breath, you inhale more or less clean air and exhale quite a lot of viruses. Soon, you are inhaling some previously exhaled viruses back and some of those might infect an additional lung cell.  By breathing through SCUBA, there are no previously exhaled viruses and therefore this R0IC should go down slightly, shouldn’t it? By breathing some higher oxygen concentrations than normal, this R0IC should go down even more. Since oxygen is a bit toxic for COVID-19.

By breathing some WARMER air than normal, this R0IC should go down even more, since the COVID-19 virus doesn’t like hot air, does it? Especially if the air is salty or smells of some detergent, pure alcohol and so on, it’s killing the viruses. Some even inside your nose and downward, perhaps.

Then, you may, sometimes after infection, during the asymptomatic phase, run up the hill in sunny weather. Puffing like an old locomotive, you will exhale a lot of viruses. Fortunately, nobody is with you and those exhaled viruses will die under the Sun. Again, you even so slightly decreased the R0IC factor and “flattened the curve” of the internal infection between your cells. You may as well try to inhale some eucalyptus hot vapors under the towel, as they suggest already. Perhaps you should insulate yourself in a sauna. Not too hot, not too humid, but just enough for you to survive and not the virus. Under medical control, of course!

And then perhaps, medical doctors should think about their doctrinal procedures for COVID-19 in this light and to refine these suggestions above considerably. I am no medical doctor! But then again, Marylin Vos Savant was no mathematician either but gave a valuable lesson to Paul Erdos himself. There are times when IQ matters the most.

Anyway. When and if you are infected with COVID-19, in the presymptomatic phase, keep the R0IC down as much as you possibly can. The second symptomatic phase may never come. Doing so, you will (ever so slightly) lower the R0 too!

DISCLAIMER: This is not official medical advice, not even unofficial medical advice. Contact your MD if or when feel ill!

Dinner with Peter Florjančič

It was today. He is a legend, 99 years old. He invented airbags so early, that his royalties would expire before they started to put them in cars. But earned a lot of money with his other inventions which are many. He knew everyone from Habsburgs to Yugoslavia’s royal family (as a child), Faruk of Egipt, almost every big European and some American businessmen, was a Chaplin’s neighbor in Switzerland ( as an adult)… A lot of photos of a lucky and brilliant man among the international jet-set.

He said he was lucky, I said that the luck is responsible for at most the half of it, the rest was his brilliance, which is genetic. Which is a kind of luck, too, I admit.

Many interesting anecdotes, but not as interesting as his cleverness in problems solving. Problems spotting at the first place, maybe. Where to substitute wood with plastics and make millions? How to spray perfumes? For hundreds of years, nobody bothered with this problem. But he did and solved it.

Then we spoke about AI. Which isn’t as clever as he was in his prime days, but it’s about to become. I didn’t formulate this so directly but he understood it anyway, I guess. I don’t think he believed that. Or even considered it remotely plausible for a second. I told him, that I am not promising him anything.  Only that chess has fallen recently and that when chemistry will fall too, there will be no more medical problems anymore. He expressed some deep general pessimism then, which I hate to see, for may it be a bad omen. To whom express it.

His life minus his daughter’s tragic death was as good as a man’s life can be.

algorithms, artificial intelligence

AI Skeptics

I am talking about those goalpost-moving crowd which says “You will be never able to make computers play chess!”. When computers do chess, they just move this goal to something else unachievable according to them, like Go. Pretending meanwhile, how trivial the chess was. It’s just an algorithm, they say.

It’s a well-known hypocrisy of this particular sect, nothing new here. But can we somehow use this pile of dishonest intellectual garbage for something interesting and informative?

Let me try! Until we have no algorithm, we have an open and “impossible” AI problem. Then, we have at least an lousy algorithm. Then we have a better algorithm. Then we have a superhuman level solving algorithm. Therefore, one day we will have the so-called AGI, when we will have one billion or more algorithms stacked so nifty, that they will trigger the most promising one among them, to solve any problem which may appear. A new algorithm will be devised when needed. In their free time, all those algorithms will be under optimization process and re-stacked often. Every aspect of this algorithm-hive will be the subject of a constant effort to improve.

And this we will call AGI. The above-mentioned skeptic club will call it “an increasingly large pile of self-improving algorithms for various tasks, nothing new”.




algorithms, artificial intelligence

Doctors and nurses and such …

… are notoriously difficult to schedule.  The right amount of them at every moment of the day or night, each working at some acceptable pace, about the right number of hours per month, with various absences, holidays and much more is a par excellence hard to plan.

If is it more chess-like complicated or Go-like complicated, depends on a particular working place in question, but it’s almost always complicated!  Human schedulers are surprisingly good, as human chess players are surprisingly good. But only to a point when the machine with the algorithm arrives. A human is no match for the top engines.

There is a superhuman level scheduler called WoShi now. Partly responsible for the hiatus we had on this blog. We are field testing it right now.




Coin Flipping Problem

Elo from LessWrong suggested this problem:

I write a sequence of n heads or tails on paper.

I then start flipping a sequence of n coins. If next coin does not match my sequence, I restart a new sequence of n coins.

What is the rule for the relationship between how many coins I need to flip to get the sequence I have pre-committed to and the length of the sequence of?

Discussion there:



Sleeping Beauty Problem Variant

Say, it’s you who is the Sleeping Beauty, awaken and told by the dungeon master:

Here is a fair coin. I will toss it and if it lands head up, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.

If the coin lands tails up, however, you’ll get this fair coin to play with as long as you wish. After then, you will be asked for a number. If that number is equal to the number of times you have been awakened like this, you will be freed.

If your number isn’t right, your memories will be erased and you will be put to sleep again and then you’ll wake up after some time in this exactly the same scenario.

What is your strategy to be freed? If not this time, but eventually?

You know that this dungeon master is telling you the truth. So this may be your first time or the second or the Nth time.

What is your best strategy to escape?

Talk about it here: