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The P vs NP problem

See original post at cdixon.org – chris dixon’s blog:

One of the great unsolved questions in computer science is the P vs NP problem. It is one of the seven Millennium Prize Problems - if you solve one of them, you get $1 million and become really famous among mathematicians and computer scientists.

Here’s my non-technical interpretation of the essence of the P vs NP problem:

Can every answer that can be feasibly verified also be feasibly calculated?

What I am calling “feasible” is what computer scientists call algorithms that can run “polynomial” as opposed to “exponential” time.

There are at least four possible outcomes to the attempts to solve this problem: 1) the current situation continues – no proof of anything is found, 2) P=NP is proved true, 3) P=NP is proved false, 4) it is proved that it’s impossible to prove P=NP to be true or false.

If P=NP were proved true, there would be many serious real-world consequences. All known encryption schemes rely on the fact that prime factors of large numbers are something that can be feasibly verified but not calculated. If P=NP, that means there would also be feasible ways to calculate prime factors, and hence decrypt codes without their private keys. So if someone does prove P=NP, he or she should probably inform authorities before publishing the proof and all hell breaks loose (thanks Matt for this observation – you could also imagine a lot of conspiracy theories about what happens to scientists who try to prove P=NP..!)

Most computer scientists seem to suspect P does not equal NP. MIT computer scientist Scott Aaronson gives informal arguments against P=NP in this entertaining blog post, including this philosophical argument:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

He follows up with a much longer essay (which I found really interesting but ultimately unconvincing) on the philosophical implications of computational complexity (the field of computer science that studies questions like P vs NP).

 

The P vs NP problem

See original post at cdixon.org – chris dixon’s blog:

One of the great unsolved questions in computer science is the P vs NP problem. It is one of the seven Millennium Prize Problems - if you solve one of them, you get $1 million and become really famous among mathematicians and computer scientists.

Here’s my non-technical interpretation of the essence of the P vs NP problem:

Can every answer that can be feasibly verified also be feasibly calculated?

What I am calling “feasible” is what computer scientists call algorithms that can run “polynomial” as opposed to “exponential” time.

There are at least four possible outcomes to the attempts to solve this problem: 1) the current situation continues – no proof of anything is found, 2) P=NP is proved true, 3) P=NP is proved false, 4) it is proved that it’s impossible to prove P=NP to be true or false.

If P=NP were proved true, there would be many serious real-world consequences. All known encryption schemes rely on the fact that prime factors of large numbers are something that can be feasibly verified but not calculated. If P=NP, that means there would also be feasible ways to calculate prime factors, and hence decrypt codes without their private keys. So if someone does prove P=NP, he or she should probably inform authorities before publishing the proof and all hell breaks loose (thanks Matt for this observation – you could also imagine a lot of conspiracy theories about what happens to scientists who try to prove P=NP..!)

Most computer scientists seem to suspect P does not equal NP. MIT computer scientist Scott Aaronson gives informal arguments against P=NP in this entertaining blog post, including this philosophical argument:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

He follows up with a much longer essay (which I found really interesting but ultimately unconvincing) on the philosophical implications of computational complexity (the field of computer science that studies questions like P vs NP).

 

The P vs NP problem

See original post at cdixon.org – chris dixon’s blog:

One of the great unsolved questions in computer science is the P vs NP problem. It is one of the seven Millennium Prize Problems - if you solve one of them, you get $1 million and become really famous among mathematicians and computer scientists.

Here’s my non-technical interpretation of the essence of the P vs NP problem:

Can every answer that can be feasibly verified also be feasibly calculated?

What I am calling “feasible” is what computer scientists call algorithms that can run “polynomial” as opposed to “exponential” time.

There are at least four possible outcomes to the attempts to solve this problem: 1) the current situation continues – no proof of anything is found, 2) P=NP is proved true, 3) P=NP is proved false, 4) it is proved that it’s impossible to prove P=NP to be true or false.

If P=NP were proved true, there would be many serious real-world consequences. All known encryption schemes rely on the fact that prime factors of large numbers are something that can be feasibly verified but not calculated. If P=NP, that means there would also be feasible ways to calculate prime factors, and hence decrypt codes without their private keys. So if someone does prove P=NP, he or she should probably inform authorities before publishing the proof and all hell breaks loose (thanks Matt for this observation – you could also imagine a lot of conspiracy theories about what happens to scientists who try to prove P=NP..!)

Most computer scientists seem to suspect P does not equal NP. MIT computer scientist Scott Aaronson gives informal arguments against P=NP in this entertaining blog post, including this philosophical argument:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

He follows up with a much longer essay (which I found really interesting but ultimately unconvincing) on the philosophical implications of computational complexity (the field of computer science that studies questions like P vs NP).

 

The P vs NP problem

See original post at cdixon.org – chris dixon’s blog:

One of the great unsolved questions in computer science is the P vs NP problem. It is one of the seven Millennium Prize Problems - if you solve one of them, you get $1 million and become really famous among mathematicians and computer scientists.

Here’s my non-technical interpretation of the essence of the P vs NP problem:

Can every answer that can be feasibly verified also be feasibly calculated?

What I am calling “feasible” is what computer scientists call algorithms that can run “polynomial” as opposed to “exponential” time.

There are at least four possible outcomes to the attempts to solve this problem: 1) the current situation continues – no proof of anything is found, 2) P=NP is proved true, 3) P=NP is proved false, 4) it is proved that it’s impossible to prove P=NP to be true or false.

If P=NP were proved true, there would be many serious real-world consequences. All known encryption schemes rely on the fact that prime factors of large numbers are something that can be feasibly verified but not calculated. If P=NP, that means there would also be feasible ways to calculate prime factors, and hence decrypt codes without their private keys. So if someone does prove P=NP, he or she should probably inform authorities before publishing the proof and all hell breaks loose (thanks Matt for this observation – you could also imagine a lot of conspiracy theories about what happens to scientists who try to prove P=NP..!)

Most computer scientists seem to suspect P does not equal NP. MIT computer scientist Scott Aaronson gives informal arguments against P=NP in this entertaining blog post, including this philosophical argument:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

He follows up with a much longer essay (which I found really interesting but ultimately unconvincing) on the philosophical implications of computational complexity (the field of computer science that studies questions like P vs NP).

 

Talk to Us About Your Problems

See original post at BRYCE DOT VC:

Before lean startups there was lean manufacturing. And Toyota was the laboratory where many of these lean principles were tested for the first time at scale. 

So, I’ve been reading up on some of the first hand experiences that came from that formative time that these lean principles were being implemented. In doing so, I came across an exchange between a Toyota manager, James Wiseman, and his then supervisor, and now Toyota Worldwide chairman, Fujio Cho.

Mr. Wiseman was a seasoned factory manager who had gained tremendous experience outside of Toyota. But when he flexed the muscles he’d developed elsewhere, he found his strengths lacking. Toyota management muscle was developed through an entirely different set of exercises. This contrast was brought home one Friday in his weekly staff meeting:

Every Friday, there was a senior staff meeting. “I started out going in there and reporting some of my little successes,” says Wiseman. “One Friday, I gave a report of an activity we’d been doing”—planning the announcement of a plant expansion—“and I spoke very positively about it, I bragged a little. After two or three minutes, I sat down.

“And Mr. Cho kind of looked at me. I could see he was puzzled. He said, ‘Jim-san. We all know you are a good manager, otherwise we would not have hired you. But please talk to us about your problems so we can all work on them together.’”

This exchange speaks to me on a few levels.

First, it calls to mind how many board meetings I’ve sat through where we spend so much time high 5’ing over all the wonderful things the team has accomplished we never get to the real meat of the meeting. We review hockey stick graphs, we talk about the great partners we have lined up, we oogle over screenshots for upcoming releases.

Startup life is difficult and occasionally we need a little praise just to muster the strength to get out of bed in the morning. But, focusing solely on the positive, while problems build, means we’ll be tackling REALLY big problems together at some point instead of tackling lots of little ones all along the way.

Second, it stresses the importance of trust between a founder and their board (or advisors, investors, friends, significant other). Often, startup founders have never been CEOs before. Many have never even managed people before. Which often leads to the feeling of being in over their heads.

Admitting you’re out of your depth and need help demands a high degree of self awareness and trust from those you’ve surrounded yourself with. As new board members or investors, perhaps we should all echo the words of Mr. Cho to the founders we fund in saying “we all know you’re a good entrepreneur otherwise we wouldn’t have backed you”. 

Explicitly establishing and amplifying this baseline of trust between a founder and their funders is a deeply critical component for any highly functional relationship that’s success is predicated on problem solving. 

At Toyota the objective was never perfection, it was improvement. By discovering and discussing these problems openly many minds were able to break them down into small, incremental, finely tuned improvements. Which ultimately yielded massively impactful results. 

Your startup isn’t Toyota, but the same principles of trust and problem solving apply. And similarly impactful results await those who talk about, and go to work solving, their problems.

Talk to Us About Your Problems

See original post at BRYCE DOT VC:

Before lean startups there was lean manufacturing. And Toyota was the laboratory where many of these lean principles were tested for the first time at scale. 

So, I’ve been reading up on some of the first hand experiences that came from that formative time that these lean principles were being implemented. In doing so, I came across an exchange between a Toyota manager, James Wiseman, and his then supervisor, and now Toyota Worldwide chairman, Fujio Cho.

Mr. Wiseman was a seasoned factory manager who had gained tremendous experience outside of Toyota. But when he flexed the muscles he’d developed elsewhere, he found his strengths lacking. Toyota management muscle was developed through an entirely different set of exercises. This contrast was brought home one Friday in his weekly staff meeting:

Every Friday, there was a senior staff meeting. “I started out going in there and reporting some of my little successes,” says Wiseman. “One Friday, I gave a report of an activity we’d been doing”—planning the announcement of a plant expansion—“and I spoke very positively about it, I bragged a little. After two or three minutes, I sat down.

“And Mr. Cho kind of looked at me. I could see he was puzzled. He said, ‘Jim-san. We all know you are a good manager, otherwise we would not have hired you. But please talk to us about your problems so we can all work on them together.’”

This exchange speaks to me on a few levels.

First, it calls to mind how many board meetings I’ve sat through where we spend so much time high 5’ing over all the wonderful things the team has accomplished we never get to the real meat of the meeting. We review hockey stick graphs, we talk about the great partners we have lined up, we oogle over screenshots for upcoming releases.

Startup life is difficult and occasionally we need a little praise just to muster the strength to get out of bed in the morning. But, focusing solely on the positive, while problems build, means we’ll be tackling REALLY big problems together at some point instead of tackling lots of little ones all along the way.

Second, it stresses the importance of trust between a founder and their board (or advisors, investors, friends, significant other). Often, startup founders have never been CEOs before. Many have never even managed people before. Which often leads to the feeling of being in over their heads.

Admitting you’re out of your depth and need help demands a high degree of self awareness and trust from those you’ve surrounded yourself with. As new board members or investors, perhaps we should all echo the words of Mr. Cho to the founders we fund in saying “we all know you’re a good entrepreneur otherwise we wouldn’t have backed you”. 

Explicitly establishing and amplifying this baseline of trust between a founder and their funders is a deeply critical component for any highly functional relationship that’s success is predicated on problem solving. 

At Toyota the objective was never perfection, it was improvement. By discovering and discussing these problems openly many minds were able to break them down into small, incremental, finely tuned improvements. Which ultimately yielded massively impactful results. 

Your startup isn’t Toyota, but the same principles of trust and problem solving apply. And similarly impactful results await those who talk about, and go to work solving, their problems.

The P vs NP problem

See original post at cdixon.org – chris dixon’s blog:

One of the great unsolved questions in computer science is the P vs NP problem. It is one of the seven Millennium Prize Problems - if you solve one of them, you get $1 million and become really famous among mathematicians and computer scientists.

Here’s my non-technical interpretation of the essence of the P vs NP problem:

Can every answer that can be feasibly verified also be feasibly calculated?

What I am calling “feasible” is what computer scientists call algorithms that can run “polynomial” as opposed to “exponential” time.

There are at least four possible outcomes to the attempts to solve this problem: 1) the current situation continues – no proof of anything is found, 2) P=NP is proved true, 3) P=NP is proved false, 4) it is proved that it’s impossible to prove P=NP to be true or false.

If P=NP were proved true, there would be many serious real-world consequences. All known encryption schemes rely on the fact that prime factors of large numbers are something that can be feasibly verified but not calculated. If P=NP, that means there would also be feasible ways to calculate prime factors, and hence decrypt codes without their private keys. So if someone does prove P=NP, he or she should probably inform authorities before publishing the proof and all hell breaks loose (thanks Matt for this observation – you could also imagine a lot of conspiracy theories about what happens to scientists who try to prove P=NP..!)

Most computer scientists seem to suspect P does not equal NP. MIT computer scientist Scott Aaronson gives informal arguments against P=NP in this entertaining blog post, including this philosophical argument:

If P=NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in “creative leaps,” no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss; everyone who could recognize a good investment strategy would be Warren Buffett. It’s possible to put the point in Darwinian terms: if this is the sort of universe we inhabited, why wouldn’t we already have evolved to take advantage of it?

He follows up with a much longer essay (which I found really interesting but ultimately unconvincing) on the philosophical implications of computational complexity (the field of computer science that studies questions like P vs NP).

 

Photo

See original post at BRYCE DOT VC:

How to convince a startup to hire you

See original post at A Smart Bear: Startups and Marketing for Geeks:

This is part of an ongoing startup advice series where I answer (anonymized!) questions from readers, like a written version of Smart Bear Live. To get your question answered, email me at asmartbear -at- shortmail -dot- com.

Ambitious Sailor writes:

How can a former navy officer with twelve solid years of overseas defense contracting experience convince a tech startup to hire him as their business guy?

I’m currently talking to [CEO] at [hot new tech company] and I have an interview coming up.

I have a love of entrepreneurship and I figured I may be able to learn a few things from smarter people than myself.

Replace your question with “why” instead of “how:”

Why should a former navy officer with overseas defense contracting experience be “the business guy” at a startup? Especially a hot tech startup?

My guess is, if you’re honest, the fact is that there is no particular reason you should be the CEO of that company. Which is why you’re asking me how to convince them otherwise.

But that’s not to say you shouldn’t be! There or somewhere. The question is not “how to convince,” the challenge is this:

Define the startup in which you would be the perfect person to be CEO or Biz Dev. Not just “OK,” not just “no reason why you couldn’t,” but perfect. No one one Earth better. Construct one startup like that — an imaginary startup.

Who would the founders be? (Probably technical with no sales or business experience, so they need someone for that role.)

What industry would it be? (Probably defense, a place where you have to “know someone” and “know how the game is played” to participate at all, where the founders aren’t those people, so they’re dead unless someone like you runs sales.)

What type of product would it be? Technical? Administrative? Mission-critical? Think hard — a startup doing something mission critical is a hard sell. What kind of product could you sell with your eyes closed

Where is the startup? (e.g. maybe it’s not near Washington, but washington is where everything goes down and you don’t mind being there, so they need you there.)

Keep going, what else? You don’t mind travel; what kind of biz dev or sales requires overseas travel that you can do cold but the founders would be bewildered?

Of course I’m ignorant of this whole industry so it’s quite likely I’m not even in the right ballpark with any of those ideas. But the mindset is right.

Now, does the startup you find have to match exactly on every point? No. But now you know what you’re looking for.

And, once you find it, you’ll get the job. If not, they’re the crazy ones.

Add your advice to the discussion section!


Sign up for AppSumo‘s daily deals specifically for web geeks & entrepreneurs.

How to convince a startup to hire you

See original post at A Smart Bear: Startups and Marketing for Geeks:

This is part of an ongoing startup advice series where I answer (anonymized!) questions from readers, like a written version of Smart Bear Live. To get your question answered, email me at asmartbear -at- shortmail -dot- com.

Ambitious Sailor writes:

How can a former navy officer with twelve solid years of overseas defense contracting experience convince a tech startup to hire him as their business guy?

I’m currently talking to [CEO] at [hot new tech company] and I have an interview coming up.

I have a love of entrepreneurship and I figured I may be able to learn a few things from smarter people than myself.

Replace your question with “why” instead of “how:”

Why should a former navy officer with overseas defense contracting experience be “the business guy” at a startup? Especially a hot tech startup?

My guess is, if you’re honest, the fact is that there is no particular reason you should be the CEO of that company. Which is why you’re asking me how to convince them otherwise.

But that’s not to say you shouldn’t be! There or somewhere. The question is not “how to convince,” the challenge is this:

Define the startup in which you would be the perfect person to be CEO or Biz Dev. Not just “OK,” not just “no reason why you couldn’t,” but perfect. No one one Earth better. Construct one startup like that — an imaginary startup.

Who would the founders be? (Probably technical with no sales or business experience, so they need someone for that role.)

What industry would it be? (Probably defense, a place where you have to “know someone” and “know how the game is played” to participate at all, where the founders aren’t those people, so they’re dead unless someone like you runs sales.)

What type of product would it be? Technical? Administrative? Mission-critical? Think hard — a startup doing something mission critical is a hard sell. What kind of product could you sell with your eyes closed

Where is the startup? (e.g. maybe it’s not near Washington, but washington is where everything goes down and you don’t mind being there, so they need you there.)

Keep going, what else? You don’t mind travel; what kind of biz dev or sales requires overseas travel that you can do cold but the founders would be bewildered?

Of course I’m ignorant of this whole industry so it’s quite likely I’m not even in the right ballpark with any of those ideas. But the mindset is right.

Now, does the startup you find have to match exactly on every point? No. But now you know what you’re looking for.

And, once you find it, you’ll get the job. If not, they’re the crazy ones.

Add your advice to the discussion section!


Sign up for AppSumo‘s daily deals specifically for web geeks & entrepreneurs.

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