Categories

## Math Tells

How to tell what part of math you are from

Gerolamo Cardano is often credited with introducing the notion of complex numbers. In 1545, he wrote a book titled Ars Magna. He introduced us to numbers like ${sqrt{-5}}$ in his quest to understand solutions to equations. Cardano was often short of money and gambled and played a certain board game to make money—see the second paragraph here.

Today, for amusement, Ken and I thought we’d talk about tells.

What are tells? Wikipedia says:

A tell in poker is a change in a player’s behavior or demeanor that is claimed by some to give clues to that player’s assessment of their hand.

## Other Tells

Ken and I have been thinking of tells in a wider sense—when and whether one can declare inferences amid uncertain information. Historians face this all the time. So do biographers, at least when their subjects are no longer living. We would also like to make inferences in our current world, such as about the pandemic. The stakes can be higher than in poker. In poker, if your “tell” inference is wrong and you lose, you can play another hand—unless you went all in. With science and other academic areas the attitude must be that you’re all-in all the time.

Cardano furnishes several instances. Wikipedia—which we regard as an equilibrium of opinions—says that Cardano

acknowledged the existence of imaginary numbers … [but] did not understand their properties, [which were] described for the first time by his Italian contemporary Rafael Bombelli.

This is a negative inference from how one of Cardano’s books stops short of treating imaginary numbers as objects that follow rules.

There are also questions about whether Cardano can be considered “the father of probability” ahead of Blaise Pascal and Pierre de Fermat. Part of the problem is that Cardano’s own writings late in life recounted his first erroneous reasonings as well as final understanding in a Hamlet-like fashion. Wikipedia doubts whether he really knew the rule of multiplying probabilities of independent events, whereas the essay by Prakash Gorroochurn cited there convinces us that he did. Similar doubt extends to how much Cardano knew about the natural sciences, as correct inferences (such as mountains with seashell fossils having once been underwater) are mixed in with what we today regard as howlers.

Every staging of Shakespeare’s Hamlet shows a book by Cardano—or does it? In Act II, scene 2, Polonius asks, “What do you read, my lord?”; to which Hamlet first replies “Words words words.” Pressed on the book’s topic, Hamlet perhaps references the section “Misery of Old Age” in Cardano’s 1543 book De Consolatione but what he says is so elliptical it is hard to tell. The book also includes particular allusions between sleep and death that go into Hamlet’s soliloquy opening Act III. The book had been published in England in 1573 as Cardan’s Comfort under the aegis of the Earl of Oxford so it was well-known. Yet the writer Italo Calvino held back from the inference:

To conclude from this that the book read by Hamlet is definitely Cardano, as is held by some scholars of Shakespeare’s sources, is perhaps unjustified.

To be sure, there are some who believe Shakespeare’s main source was Oxford, in manuscripts if not flesh and blood. One reason we do not go there is that we do not see the wider community as having been able to establish reliable principles for judging what kinds of inferences are probably valid. We wonder if one could do an experiment of taking resolved cases, removing most of the information to take them down to the level of unresolved cases, and seeing what kinds of inferences from partial information would have worked. That’s not our expertise, but within our expertise in math and CS, we wonder if a little experiment will be helpful.

To set the idea, note that imaginary numbers are also called complex numbers. Yet the term complex numbers can mean other things. Besides numbers like ${2 + 3i}$ it also can mean how hard it is to construct a number.

In number theory, the integer complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions, multiplications, and parentheses. It is always within a constant factor of the logarithm of the given integer.

How easy is it to tell what kind of “complex” is meant if you only have partial information? We don’t only mean scope-of-terminology issues; often a well-defined math object is used in multiple areas. Let’s try an experiment.

## Math Tells

Suppose you walk in log-in to a talk without any idea of the topic. If the speaker uses one of these terms can you tell what her talk might be about? Several have multiple meanings. What are some of them? A passing score is ${dots}$

1. She says let ${S}$ be a c.e. set.
2. She says let ${k}$ be in ${omega}$.
3. She says by the König principle.
4. She says ${S}$ is a prime.
5. She says ${n}$ is a prime.
6. She says ${G}$ is solvable.
7. She says let its degree be ${0}$.
8. She says there is a run.
9. She says it is reducible.
10. She says it is satisfiable.

Categories

## J.K. Rowling is four cocktails in and talking trash about Bitcoin

J.K. Rowling has been drinking a lot and you’d better believe she has some thoughts on Bitcoin.
NotedTERF and author of The Cuckoos Calling, Rowlingdecided Friday was the perfect time to learn about…

Categories

## Math Tells

How to tell what part of math you are from

Gerolamo Cardano is often credited with introducing the notion of complex numbers. In 1545, he wrote a book titled Ars Magna. He introduced us to numbers like ${sqrt{-5}}$ in his quest to understand solutions to equations. Cardano was often short of money and gambled and played a certain board game to make money—see the second paragraph here.

Today, for amusement, Ken and I thought we’d talk about tells.

What are tells? Wikipedia says:

A tell in poker is a change in a player’s behavior or demeanor that is claimed by some to give clues to that player’s assessment of their hand.

## Other Tells

Ken and I have been thinking of tells in a wider sense—when and whether one can declare inferences amid uncertain information. Historians face this all the time. So do biographers, at least when their subjects are no longer living. We would also like to make inferences in our current world, such as about the pandemic. The stakes can be higher than in poker. In poker, if your “tell” inference is wrong and you lose, you can play another hand—unless you went all in. With science and other academic areas the attitude must be that you’re all-in all the time.

Cardano furnishes several instances. Wikipedia—which we regard as an equilibrium of opinions—says that Cardano

acknowledged the existence of imaginary numbers … [but] did not understand their properties, [which were] described for the first time by his Italian contemporary Rafael Bombelli.

This is a negative inference from how one of Cardano’s books stops short of treating imaginary numbers as objects that follow rules.

There are also questions about whether Cardano can be considered “the father of probability” ahead of Blaise Pascal and Pierre de Fermat. Part of the problem is that Cardano’s own writings late in life recounted his first erroneous reasonings as well as final understanding in a Hamlet-like fashion. Wikipedia doubts whether he really knew the rule of multiplying probabilities of independent events, whereas the essay by Prakash Gorroochurn cited there convinces us that he did. Similar doubt extends to how much Cardano knew about the natural sciences, as correct inferences (such as mountains with seashell fossils having once been underwater) are mixed in with what we today regard as howlers.

Every staging of Shakespeare’s Hamlet shows a book by Cardano—or does it? In Act II, scene 2, Polonius asks, “What do you read, my lord?”; to which Hamlet first replies “Words words words.” Pressed on the book’s topic, Hamlet perhaps references the section “Misery of Old Age” in Cardano’s 1543 book De Consolatione but what he says is so elliptical it is hard to tell. The book also includes particular allusions between sleep and death that go into Hamlet’s soliloquy opening Act III. The book had been published in England in 1573 as Cardan’s Comfort under the aegis of the Earl of Oxford so it was well-known. Yet the writer Italo Calvino held back from the inference:

To conclude from this that the book read by Hamlet is definitely Cardano, as is held by some scholars of Shakespeare’s sources, is perhaps unjustified.

To be sure, there are some who believe Shakespeare’s main source was Oxford, in manuscripts if not flesh and blood. One reason we do not go there is that we do not see the wider community as having been able to establish reliable principles for judging what kinds of inferences are probably valid. We wonder if one could do an experiment of taking resolved cases, removing most of the information to take them down to the level of unresolved cases, and seeing what kinds of inferences from partial information would have worked. That’s not our expertise, but within our expertise in math and CS, we wonder if a little experiment will be helpful.

To set the idea, note that imaginary numbers are also called complex numbers. Yet the term complex numbers can mean other things. Besides numbers like ${2 + 3i}$ it also can mean how hard it is to construct a number.

In number theory, the integer complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions, multiplications, and parentheses. It is always within a constant factor of the logarithm of the given integer.

How easy is it to tell what kind of “complex” is meant if you only have partial information? We don’t only mean scope-of-terminology issues; often a well-defined math object is used in multiple areas. Let’s try an experiment.

## Math Tells

Suppose you walk in log-in to a talk without any idea of the topic. If the speaker uses one of these terms can you tell what her talk might be about? Several have multiple meanings. What are some of them? A passing score is ${dots}$

1. She says let ${S}$ be a c.e. set.
2. She says let ${k}$ be in ${omega}$.
3. She says by the König principle.
4. She says ${S}$ is a prime.
5. She says ${n}$ is a prime.
6. She says ${G}$ is solvable.
7. She says let its degree be ${0}$.
8. She says there is a run.
9. She says it is reducible.
10. She says it is satisfiable.

Categories

## J.K. Rowling is four cocktails in and talking trash about Bitcoin

J.K. Rowling has been drinking a lot and you’d better believe she has some thoughts on Bitcoin.
NotedTERF and author of The Cuckoos Calling, Rowlingdecided Friday was the perfect time to learn about…

Categories

## Charles Hoskinson Explains How Cardano Could Get to a Trillion Dollar Market Cap

Charles Hoskinson explains how Cardano will get to a trillion dollar market cap.

23098 Total views

249 Total shares

In a recent interview with Cointelegraph, Ethereum (ETH) co-founder and Cardano (ADA) founder Charles Hoskinson explained why he believes Cardano is poised for a trillion dollar market cap.

One of the main distinguishing points of Cardano’s development approach is its emphasis on research-first.

## Genius founder will not always be around

Though there have recently been a new crop of what Hoskinson calls “science coins” — such as Algorand (ALGO), AVA, and StarkWare — when Cardano was starting out, this approach was radically unorthodox. To this day, the approach often attracts criticism for being too academically pedantic and slow. However, Hoskinson believes that it will allow Cardano to shine in the future:

“So my whole argument for academic rigour is it’s not just about today, it’s about tomorrow in two different respects. It’s about tomorrow from the respect that we can get protocols that can scale to billions of users. And there are no protocols in the world that right now allow us to do that. So they have to be designed. And then two, who will come up with the protocols five years from now, 10 years from 15 years from now? Are we always going to have the genius founder around? No.”

## Scaling to billion users

In order to make sure that the project can function and grow even without its “genius” founder, a project needs to create “a decentralized brain” that will enable perpetual innovation:

“So when quantum computers come alive, we have defenses against that. When we start doing these things on satellites, we have protocols for that. Well, we want these things to work on a cell phone with the same user experience and use recursive snarks. <...> And it doesn’t have to be built by one company or one party. It can come out of the academic world in a very decentralized way. <...> So I think this is the long term superior approach and it’s the only approach that will actually get us to the protocol of a billion people.”

## Getting to trillion dollar cap

Hoskinson believes it is just a matter of time before the crypto industry will grow from billions to trillions. One key driver of this growth is demographics:

“First key point here is that everybody under the age of 35. If you take a cross-section of them, statistically speaking from McKinsey and these other people are more likely to own a cryptocurrency than own a bond, a stock or gold. So investor interest in this asset class is biased towards [the] young. And as the young get older, they get richer.”

Furthermore, Hoskinson expects governments to start adopting blockchain technology and at the same time, provide clearer regulation:

“Eventually, states will run their voting systems. Eventually states where their property registration, all these things. So the fact that those systems exist and they’re doing all these things creates more inflow of value. And third, the regulations are getting set that institutional investors can finally put money into our industry, which brings billions of dollars of new investment.”

And when all of these factors align, Hoskinson believes that Cardano will be positioned to benefit the most:

“And I think we are best positioned to capture the largest chunk long term. Now, whether that happens in five years, 10 years, 15 years, a whole bunch of things could occur to accelerate or put the brakes on our entire movement.”

Many in the crypto community agree that the crypto industry could eventually grow to the trillion dollar range, but only time will tell whether Cardano will be the main beneficiary of such a spurt.

Categories

## J.K. Rowling is four cocktails in and talking trash about Bitcoin

J.K. Rowling has been drinking a lot and you’d better believe she has some thoughts on Bitcoin.
NotedTERF and author of The Cuckoos Calling, Rowlingdecided Friday was the perfect time to learn about the cryptocurrency Bitcoin. And so, like any celebrity who …

Categories

## Charles Hoskinson Explains How Cardano Could Get to a Trillion Dollar Market Cap

Charles Hoskinson explains how Cardano will get to a trillion dollar market cap.

22720 Total views

249 Total shares

In a recent interview with Cointelegraph, Ethereum (ETH) co-founder and Cardano (ADA) founder Charles Hoskinson explained why he believes Cardano is poised for a trillion dollar market cap.

One of the main distinguishing points of Cardano’s development approach is its emphasis on research-first.

## Genius founder will not always be around

Though there have recently been a new crop of what Hoskinson calls “science coins” — such as Algorand (ALGO), AVA, and StarkWare — when Cardano was starting out, this approach was radically unorthodox. To this day, the approach often attracts criticism for being too academically pedantic and slow. However, Hoskinson believes that it will allow Cardano to shine in the future:

“So my whole argument for academic rigour is it’s not just about today, it’s about tomorrow in two different respects. It’s about tomorrow from the respect that we can get protocols that can scale to billions of users. And there are no protocols in the world that right now allow us to do that. So they have to be designed. And then two, who will come up with the protocols five years from now, 10 years from 15 years from now? Are we always going to have the genius founder around? No.”

## Scaling to billion users

In order to make sure that the project can function and grow even without its “genius” founder, a project needs to create “a decentralized brain” that will enable perpetual innovation:

“So when quantum computers come alive, we have defenses against that. When we start doing these things on satellites, we have protocols for that. Well, we want these things to work on a cell phone with the same user experience and use recursive snarks. <...> And it doesn’t have to be built by one company or one party. It can come out of the academic world in a very decentralized way. <...> So I think this is the long term superior approach and it’s the only approach that will actually get us to the protocol of a billion people.”

## Getting to trillion dollar cap

Hoskinson believes it is just a matter of time before the crypto industry will grow from billions to trillions. One key driver of this growth is demographics:

“First key point here is that everybody under the age of 35. If you take a cross-section of them, statistically speaking from McKinsey and these other people are more likely to own a cryptocurrency than own a bond, a stock or gold. So investor interest in this asset class is biased towards [the] young. And as the young get older, they get richer.”

Furthermore, Hoskinson expects governments to start adopting blockchain technology and at the same time, provide clearer regulation:

“Eventually, states will run their voting systems. Eventually states where their property registration, all these things. So the fact that those systems exist and they’re doing all these things creates more inflow of value. And third, the regulations are getting set that institutional investors can finally put money into our industry, which brings billions of dollars of new investment.”

And when all of these factors align, Hoskinson believes that Cardano will be positioned to benefit the most:

“And I think we are best positioned to capture the largest chunk long term. Now, whether that happens in five years, 10 years, 15 years, a whole bunch of things could occur to accelerate or put the brakes on our entire movement.”

Many in the crypto community agree that the crypto industry could eventually grow to the trillion dollar range, but only time will tell whether Cardano will be the main beneficiary of such a spurt.

Categories

## J.K. Rowling is four cocktails in and talking trash about Bitcoin

J.K. Rowling has been drinking a lot and you’d better believe she has some thoughts on Bitcoin.
NotedTERF and author of The Cuckoos Calling, Rowlingdecided Friday was the perfect time to learn about the cryptocurrency Bitcoin. And so, like any celebrity who …

Categories

## Charles Hoskinson Explains How Cardano Could Get to a Trillion Dollar Market Cap

Charles Hoskinson explains how Cardano will get to a trillion dollar market cap.

22123 Total views

249 Total shares

In a recent interview with Cointelegraph, Ethereum (ETH) co-founder and Cardano (ADA) founder Charles Hoskinson explained why he believes Cardano is poised for a trillion dollar market cap.

One of the main distinguishing points of Cardano’s development approach is its emphasis on research-first.

## Genius founder will not always be around

Though there have recently been a new crop of what Hoskinson calls “science coins” — such as Algorand (ALGO), AVA, and StarkWare — when Cardano was starting out, this approach was radically unorthodox. To this day, the approach often attracts criticism for being too academically pedantic and slow. However, Hoskinson believes that it will allow Cardano to shine in the future:

“So my whole argument for academic rigour is it’s not just about today, it’s about tomorrow in two different respects. It’s about tomorrow from the respect that we can get protocols that can scale to billions of users. And there are no protocols in the world that right now allow us to do that. So they have to be designed. And then two, who will come up with the protocols five years from now, 10 years from 15 years from now? Are we always going to have the genius founder around? No.”

## Scaling to billion users

In order to make sure that the project can function and grow even without its “genius” founder, a project needs to create “a decentralized brain” that will enable perpetual innovation:

“So when quantum computers come alive, we have defenses against that. When we start doing these things on satellites, we have protocols for that. Well, we want these things to work on a cell phone with the same user experience and use recursive snarks. <...> And it doesn’t have to be built by one company or one party. It can come out of the academic world in a very decentralized way. <...> So I think this is the long term superior approach and it’s the only approach that will actually get us to the protocol of a billion people.”

## Getting to trillion dollar cap

Hoskinson believes it is just a matter of time before the crypto industry will grow from billions to trillions. One key driver of this growth is demographics:

“First key point here is that everybody under the age of 35. If you take a cross-section of them, statistically speaking from McKinsey and these other people are more likely to own a cryptocurrency than own a bond, a stock or gold. So investor interest in this asset class is biased towards [the] young. And as the young get older, they get richer.”

Furthermore, Hoskinson expects governments to start adopting blockchain technology and at the same time, provide clearer regulation:

“Eventually, states will run their voting systems. Eventually states where their property registration, all these things. So the fact that those systems exist and they’re doing all these things creates more inflow of value. And third, the regulations are getting set that institutional investors can finally put money into our industry, which brings billions of dollars of new investment.”

And when all of these factors align, Hoskinson believes that Cardano will be positioned to benefit the most:

“And I think we are best positioned to capture the largest chunk long term. Now, whether that happens in five years, 10 years, 15 years, a whole bunch of things could occur to accelerate or put the brakes on our entire movement.”

Many in the crypto community agree that the crypto industry could eventually grow to the trillion dollar range, but only time will tell whether Cardano will be the main beneficiary of such a spurt.

Categories

## J.K. Rowling is four cocktails in and talking trash about Bitcoin

J.K. Rowling has been drinking a lot and you’d better believe she has some thoughts on Bitcoin.
NotedTERF and author of The Cuckoos Calling, Rowlingdecided Friday was the perfect time to learn about the cryptocurrency Bitcoin. And so, like any celebrity who …