I didn't say that imaginary numbers don't have a use. I said that I cannot have an imaginary number of apples in my fridge. — Michael

Well, you said that as if it makes a point. Which escapes my simple mind.

Yes, and this premise is proven false. See refutation by contradiction and modus tollens. — Michael

If after all this, your point is that Thompson's lamp is a silly thought experiment, at long last we are in full agreement. It doesn't tell you much about supertasks, though. Perhaps I should have tried to expand on that line of argument earlier. Thompson's lamp is not a good example of a supertask, because the sequence doesn't have a limit or any natural termination point.

Zeno getting up from the couch to get a snack in the kitchen, under the assumption of arbitrary divisibility of time and space, is a much better example. I have argued that that is a true supertask, one that is metaphysically possible.

But I was thinking about your button presses. I don't see why the sequence doesn't run at every time prior to midnight; and then at exactly midnight, the Supreme Button Pusher doesn't just flip a coin and turn the lamp on or off accordingly. Makes as much sense as the rest of the story.

It doesn't refute my argument because it doesn't address my argument. — Michael

It (my inverse powers of 2 model) shows that at any time prior to midnight, we know the state of the lamp. And that at midnight, it's undefined and entirely arbitrary.

My argument is that the lamp cannot be on unless it is turned on (whether by pushing a button or by magic), as argued above. — Michael

Ok. At midnight the Supreme Button Pusher flips a coin and turns the lamp on or off, accordingly. I don't see any problem.

Therefore, off, on, off, ..., on makes no sense in context. The lamp being off must precede the lamp being on. — Michael

Not at the termination point. Only prior to midnight. Not AT midnight. As I've indicated. It's fundamental to the nature of an infinite sequence with a termination point adjoined at the end.

Given that this is inconsistent with the premise that the button is pushed at successively halved intervals of time it is proven impossible in principle to push the button at successively halved intervals of time. — Michael

No no no no no. "the premise that the button is pushed at successively halved intervals of time" is only valid for the infinite sequence itself, and NOT for the termination point.

Yeah, the day one of the worst presidents in history gets shot — Mikie

Wow. I'm speechless. Dare I ask why you say that? But nevermind. I don't necessarily need to have this conversation.

You'll ignore a summer of deadly rioting
— fishfry

Hysterical. Childish. — Mikie

Really? "However, arson, vandalism, and looting that occurred between May 26 and June 8 caused approximately $1–2 billion in insured damages nationally, the highest recorded damage from civil disorder in U.S. history, and surpassing the record set during the 1992 Los Angeles riots." -- Wiki

And: "By the end of June 2020, at least 14,000 people had been arrested. By June 2020, more than 19 people had died in relation to the unrest." -- Wiki

But at least it wasn't the guy in horns wandering aimlessly around the capitol. That was an insurrection.

As I said earlier, I've got the points bundled into a continuous line, but not all of the points can be isolated. So if by 'completeness' you mean a line without gaps then my line is complete. However, if by 'completeness' you mean a line that can be described as the disjoint union of infinite points/numbers then my line is incomplete. — keystone

If there are no gaps, it's complete. That's the informal definition. The official definition is that every Cauchy sequence converges. You haven't defined Cauchy sequences so I don't know.

What you are essentially saying is that a turing machine cannot operate on an infinite memory tape since such a tape cannot exist in a finite world. Ok, you're right. — keystone

Right, all physical computers have bounded resources.

I largely agree but I would phrase it as 'there is no smallest possible positive number'. This distinction is important if numbers are emergent but it's not worth discussing at this time. — keystone

Hmmm, murky.

Let me rephrase my argument to address these points you've made.
...
Is that more clear now? — keystone

I believe you are doing computer math. Well known. I believe you are describing IEEE-754 floating point numbers. There is a smallest and largest possible value. It's actually not even hardware dependent, it's in the standard.

https://en.wikipedia.org/wiki/Fixed-point_arithmetic

Or you might be describing fixed point numbers.

https://en.wikipedia.org/wiki/Fixed-point_arithmetic

Either way you're doing computer arithmetic, where there is a minimum smallest interval and even a largest possible number.

Way way short of being the real numbers. So you can do approximate calculus or discrete calculus that way if you like. I think this is what you are getting at.

Am I close?

As always, I'm grateful for this discussion and I'm certainly not complaining, but I hope you see that I have to walk a very thin line with you. — keystone

It's ok, I have my second wind I think. Especially now that I know you're just doing computer arithmetic, fixed or floating point.

I can't talk too high level as you will ask for the beef, I can't show figures as they will make your eyes glaze over, I can't use analogies because my analogies don't stick, and when I try to talk technical you often skip over or misunderstand my ideas. — keystone

Yes! Now we're communicating :-)

Of course, it doesn't help that I'm not a trained mathematician. Again, I'm extremely grateful for this discussion, just trying to put things in perspective. — keystone

If you're doing computer arithmetic or some variant, we're on the same page.

1) Get you to agree to my use of ε in the computer example (including understand the illustration).
2) Get you to agree to my use of ε in the pi example (including understand the illustration).
3) Progress to 2D, where the Cartesian Coordinate system is replaced with a top-down alternative, and the zeros of y=x^2-2 have a very different meaning. Illustrations become important here which is why we need to get past 1) and 2) first.
4) Top-down interpretation of calculus. — keystone

I'll stipulate that you can do discrete calculus on a computer.

https://en.wikipedia.org/wiki/Discrete_calculus

Hopefully this plan will at least give you confidence that I'm heading somewhere with all of this... — keystone

Well if we're doing computer arithmetic and some variant of discrete calculus, that's interesting to know. What do you think?

The subpoena to Garland was pure theatre and retribution — Wayfarer

Just grabbing this quote for tagging purposes, perhaps I'll get to the particulars later. I want to be more general today.

Your posts have been on my mind. I have a desire to explain myself, and explain Trump, to liberals who hate him. I'm a fallen liberal. I voted for Carter, for the useless Mondale and Dukakis. For Kerry, who said he'd "Fight the war, but better," at a time when the country longed for someone to shut down that illegal and immoral war. A war supported by Hillary and all the other prominent Dems at the time. That was just one of many data points along the way to my growing disaffection with and now my total defection from the Democratic party.

I voted for every Democrat in every election in my lifetime, until I voted for Trump. Even then it was more of a protest vote. I live in California, which goes Democrat no matter what. I often have the luxury of a meaningless protest vote. At the time I asked myself what I'd do if I lived in a swing state. Probably vote for Hillary. Maybe not. It was close.

But after the behavior and actions of the Democrats since 2016, I and many other doubtful and trepidatious Trump voters of 2016 have had our positions hardened. It's not that I don't see Trump's many faults. But the Democrats have gone off the deep end. Some call it TDS. Looking the other way on too many bad ideas and too much outright evil because they hate the Orange Man. The monster that, ironically, they created themselves. Just look at his post-conviction polls. The more corrupt lawfare, the more Americans peel away from the Democrats. If you'd ignored him you'd be beating DeSantis by now.

Anyway I realize that I can't write my grand unified theory of Trump and how it relates to my own political development, all in one post. There's too much.

Instead I'll just try to write a little at a time, inspired that someone like as yourself has curiosity about what I have to say. I think this is the first time that's ever happened. Usually it's just abuse. "Let me explain what people see in Trump." "You Trumpers all suck." I'm sure you've seen the pattern. After a while, you come to see the nature of Trump's opposition, and you have to support the guy because there is no alternative.

So when you wrote about "the despicable actions of Trump and his flunkeys," yet you still want to hear what I have to say, then that's one more listener than I had yesterday. I thank you for that.

Before going on with generalities, I want to push back on the word despicable.

The Biden administration is running the world's largest child trafficking operation at the southern border. They've lost track of 1 out of ever 4 children. "Separating families" is bad, the lefties screech. Instead, they just let everyone in. "Oh, this is your child? Come on in." The reason you separate families is not to be cruel. It's to weed out the traffickers. Liberals who don't know the first thing about the southern border have no clue. The cartels are thriving. I say that's despicable.

If you say that's just a right wing talking point, you are wrong. I know border issues. Liberals are in denial about the horrific human rights abuses Biden is enabling. Shame on the MSM that let you stay asleep, and on the Democrats and liberals who prefer not to know.

Please don't think that only one politician or party in the US is despicable.

Ok end of that rant.

Something bad happened to the left after 2016. They call it TDS. I believe it. I see the left doing very foolish and dangerous things because they hate Trump so much. The open borders, the decriminalization of crime, and the bumbling and potentially fatal foreign policy.

Trump had four years of peace and was the only president in my lifetime not to start a new war. You think that was an accident? It's something many Americans long for. It was no accident.

Another funny thing. The Trump monster is of the Dems' own making. A year ago we were all tired of Trump. I was tired of Trump, and I'm a good barometer for that. I thought DeSantis would be the nominee. Then they raided Mar-a-Lago, and the next day DeSantis was forced to come out in Trump's defense, then he faded in the polls, and Trump rocketed on up. Dems, YOU did this. We all thought Trump was done. You breathed life into him through your corrupt lawfare and political attacks.

Do you not see the irony? Do you not look at the polls? If you'd left Trump alone, DeSantis or dog killer Noem would be the GOP nominee and they'd both lose. By the way I hate the Republicans even more than the Democrats, if you're wondering. The Republicans are so effing useless. I remember when they spent six years railing against Obamacare. Then they woke up in 2017 and found themselves in possession of the Presidency, the Senate, and the House. It immediately became obvious that they hadn't spent five minutes in all those years thinking about health care policy. In the end they failed to overturn it.

Hopeless. The gang that can't shoot straight.

The Dems have become the evil party, and the GOP the useless party. What's an independent-minded free thinker like me to do? It's Trump, brother. He's all there is. There isn't another. And he's up against the entire establishment. It's something to behold. People are starting to be drawn to his epic struggle.

I tell you, the Dems have created the very monster they fear.

Bottom line: I am one of the ten million or so Americans who voted for Obama and then voted for Trump. Reluctantly at first. And then, watching the Dems and liberals after 2016, now enthusiastically. Not because I don't see Trump's many faults. Not even because I like him. Many of Trump's supporters don't like him much. But right now, he is the only game in town. I wish it were not so. It's where the Dems have brought us.

And really, @Wayfarer, would you like to pretend to sell me on the virtues of that desiccated husk of the stupid and corrupt career politician they call Biden? Did you see him yesterday at Normandy?

Is that what you're selling me? Sorry, I've seen the goods.

Biden's staff evidently studied Reagan's 1984 speech, as reported by Politico and the NYT; and even plagiarized parts of it, as reported by some scurrilous right wingers who watched both speeches side by side. I haven't personally verified that last bit. Fitting for known plagiarist Biden. @Benkei you did cast a disparaging eye on Reagan, did you not? Ironic that he was the go-to inspiration for your guy yesterday. And he failed miserably of course. I suppose I should ask you the same question: You sellin' me four more years of that?

Since 2016 very few if any Democrats have troubled to ask themselves the question, who voted for Democrats all their lives, then voted for Trump?

They didn't ask that. Instead Hillary commissioned the fake Steele dossier, misreported the expense (ahem) and started the past eight years of vicious political lawfare against the Great Orange Monster.

And only made him stronger in the process.

I am a lifelong liberal and registered Democrat. And liberals and Democrats, you terrify me.

to see intelligent people rationalizing the despicable
actions of Trump and his flunkeys. It’s depressing. — Wayfarer

I see intelligent people on the left, where I used to be, rationalizing lawfare and the politicized application of justice, from Russiagate to the present moment. I'm profoundly depressed about it. You gloated about Bannon but ignored my question about Holder. And now Garland is doing the same, refusing to honor a Congressional subpoena.

I came to the Trump thread to speak for Trump's Constitutional rights; and not for the man himself. I regret getting drawn into irrelevancies. He is not on trial for J6 and I did not post abou J6. And for what it's worth, I deny it was an "insurrection." That's a childish and false charge, especially in view of the summer of leftist riots that preceded it.

"To my friends, everything; to my enemies, the law."

dumb as fuck — Benkei

Just can't help yourself. Done with you

You're so dumb — Benkei

Have a nice evening. Your inability to engage in intelligent conversation is apparent to all.

I said attempt. And no, it's not hysterical. But nice try at downplaying. Does it make you sleep better? — Benkei

Hysterical. Childish.

Again, only dumb Americans don't take J6 seriously. Everybody outside saw it for what it was. A bunch of thugs trying to keep their God Emperor Trump on the throne as they have admitted to and informants in the Boogaloo, Proud Boys and other militant groups, that were there, reported on. But yeah, keep your head in the same and pretend this was the same as a riot and watch it happen again next time Trump loses. — Benkei

I expect the left to riot and rampage if Trump wins. It's the left who are the danger to democracy these days. I'll concede your next string of silly leftist talking points, which I did not come here to debate. I don't have to defend Trump. Just defending the man's Constitutional rights is enough to trigger the checkbox leftists. It's pathetic to watch. Pathetic and disheartening.

I came here to ask if people would cut down the law to get at the Devil, in response to the New York trial.

And what is the response? J6 J6 J6. Why? Because you have no response to the question. You'll ignore a summer of deadly rioting, 20 killed, billions in damages, over a violent career criminal who died of a fentanyl overdose. But the guy in the war paint, fur, and horns? That sends you into a paroxysm of rage.

You are easily played.

A riot is not an attempt to overthrow a government. — Benkei

Overthrow the government. That hysterical rhetoric is childish. Nobody overthrew the government. Handful of unarmed clowns in costumes. Guess you missed the leftists interrupting Kavanaugh hearing. Or the pro-Palestine protesters occupying Congress a few weeks ago. Selective outrage, selective application of the law.

The fact you're trying to equate them underlines the rot Wayfarer is pointing to. Bringing up Babbitt in response to the shameful treatment of chips doing their jobs, as if that excuses such a response, underlines the same rot. — Benkei

Not equating. Calling out the hypocrisy. Cop shoots protester to death, left doesn't give a shit because it was a right wing protester. If the races and political positions were reversed, it would be George Floyd all over again. A summer of looting, burning, and killing. The left condoned it. Kamala Harris started a fund for their bail. Said the riots would continue.

Take it from somebody looking at American Bullshit from the outside; it's been rotting since Reagan. — Benkei

Since November 22, 1963.

"we know the basic part of the answer — and that is, there are sequences of neuron firings and they terminate where the acetylcholine is secreted at the axon end-plates of the motor neurons, sorry to use philosophical terminology here. But when it is secreted at the axon end-plates of the motor neurons, a whole lot of wonderful things happen in the ion channels and the damned arm goes up."
That's a wordy version of what I said, which is "there's wires connecting the parts where the will is implemented, to the parts where the motor control is implemented". Under Chalmers, there isn't such a wire, hence the magic. — noAxioms

Where is the will that initiates the process?

Nobody ever said the program was conscious. It's dumb as rocks, implementing a fairly small program that simply knows how to move the particles around. It implements physics and is no more conscious than is physical law. It has no external input, so right there it doesn't qualify as being conscious. Some programs do have such input, but not most simulations. — noAxioms

You are agreeing with me again?

Anyway, you don't believe a simulated person could be conscious, so you make up an arbitrary rule that forbids it. — noAxioms

I made no rules. I expressed an opinion.

I think that's what you're saying, but personal belief isn't evidence against somebody's hypothesis. It's only an irrational reason that you don't accept the hypothesis. — noAxioms

Ok. My reasons are irrational.

You sound like I said something that annoyed you.

Thanks for keeping this brief, anyway. I didn't understand much of this particular post. The rest of this convo has been interesting.

I understand that it has no end. That is why I am arguing that it is metaphysically impossible for an infinite succession of button pushes to end after two minutes. — Michael

Who is pushing this button, by the way? And how? Magic again?

It's a premise of the thought experiment that there is a sequence of steps at successively halved intervals of time. You are now arguing that since such a premise is physically impossible, it's metaphysically impossible. You are wrong on the facts and wrong on the logic.

And its your premise, not mine.

0,1,0,...,10,1,0,...,0

Such sequences may make sense in the context of abstract mathematics but they do not make sense in the context of a lamp being turned on and off. — Michael

It's a mathematical model of a lamp being turned on and off. What if instead of a lightbulb, we have a big LED that displays 0 or 1? You have an objection to that? Based on what?

I already showed you how to model the process using the inverse powers of 2. You ignored that, since it refutes your argument.

As a comparison, even though imaginary numbers have a use in mathematics it is more than just physically impossible for me to have -1‾‾√ — Michael

Tell that to an electrical engineer or quantum physicist, both of whom use imaginary and complex numbers as essential tools of their trades.

apples in my fridge; it is metaphysically impossible. — Michael

Wow. I guess you don't believe in negative numbers, fractions, or irrational numbers either. You are really flailing with these weak arguments.

No pretend physics can allow for me to have an imaginary number of apples in my fridge and no pretend physics can allow for the above two mathematical sequences to model the state of a lamp over time. — Michael

You accept "on" and "off" but not one and zero? Again: replace the bulb with an LED that alternately flashes 1 and 0.

With Thomson's lamp, these are our premises:

P1. Nothing happens to the lamp except what is caused to happen to it by pushing the button
P2. If the lamp is off and the button is pushed then the lamp is turned on
P3. If the lamp is on and the button is pushed then the lamp is turned off
P4. The lamp is off at t0
P5. The button is pushed at least once between t0 and t1
P6. The lamp is either on or off at t1

And these are our conclusions:

C1. If the lamp is on at t1 then the button was pushed to turn it on, prior to which it was off
C2. If the lamp is off at t1 then the button was pushed to turn it off, prior to which it was on
C3. The button was pushed n∈ℕ
�
∈
�
1
times between t0 and t1

These conclusions prove that a supertask is not performed. — Michael

I must have made a pretty good argument in my previous post, since in your response you went into wild irrelevancies and repeated arguments I've long lost interest in, and never engaged with a word I said.

You really reject the complex numbers, negative numbers, fractions, and irrationals? Is mathematical nihilism your last defense?

I don't have an alternate construction of the complete set of isolated real numbers. — keystone

Then what on earth are you doing?

I don't have the intermediate value theorem or the least upper bound property. — keystone

You claimed completeness. Do you now retract that? Or have a private definition?

I acknowledge that for the bottom-up view, calculus requires the complete set of isolated real numbers, the intermediate value theorem, and the least upper bound property to "work"...I use quotes because it also requires some mental gymnastics. However, that's just not the case for the top-down view. It works perfectly in absence of all of the above...including the mental gymnastics. — keystone

How does it work? What does it do?

No such thing as an arbitrarily small positive real number.
— fishfry

Consider the following Python function:

def small_number_generator():
n = 1
while True:
print(n)
n /= 2

If executed, this function will print 1, 1/2, 1/4, 1/8, 1/16, and so on to no end. By saying that there is no smallest positive number you are essentially acknowledging that this program does not halt. — keystone

If executed, such a program will eventually output the same number over and over, until its computing resources run out. You are factually wrong and I hope you can see why. Even so, there is no smallest positive real number, and you have not provided an argument.

I agree with that. What I'm saying is that for any positive number you provide, x, I can run the code in a finite amount of time to print out a number smaller than x. In other words, it has the potential to print out a number as small as you want but it cannot actually print out the smallest positive number, any more than it can halt. Do you understand this distinction? — keystone

What? There is no smallest positive real number.

Moreover, without ever executing the program I can describe the function's potential. Assuming it will run for at least a little while, at any time the last number it will have actually printed, ε, necessarily cuts the line (0,1) as depicted below: — keystone

Not even wrong. You are talking nonsense.

Again, until we execute the function ε doesn't hold an actual value. In this illustration, ε is simply a placeholder. The fact that I drew it approximately 1/3 between 0 and 1 is inconsequential. All that can be said is that if executed, ε will correspond to a point somewhere between 0 and 1. That's how you should interpret the drawing. — keystone

There is no smallest positive real number. I see that you are confused about this.

In this light, I ask that you revisit the example from my last post and see if you understand step (3) where I plan an irrational computable cut at π. I specifically wrote plan there instead of execute because I wanted to focus on the potential of the cut, as I have done for the program illustrated above. — keystone

There is no smallest positive real number. You have convinced me that you are simply confused about this point. The real numbers are a field. You can always divide by 2.

I keep trying to advance forward but your responses continue to either directly or indirectly show that you're not following. If you don't understand what I'm illustrating when I plan an irrational computable cut at π then you won't understand my 2D illustrations that demonstrate that the IVT and the LUB property are not required for the top-down view. — keystone

Your most recent exposition postulated a smallest positive real number. There is no such thing. There is nothing for me to follow.

But even so. I have repeatedly asked you to give me the big picture. Give me something.

By the way, I don't accept that. I watched a great deal of the telecast, I found it compelling and right on target. — Wayfarer

Didn't they throw certain GOP members off the committee or deny them membership, flouting longstanding procedures? I also hear they destroyed all their records. Thousands of hours of video are still suppressed.

Trump should never be considered for public office again, in light of what he was shown to have done. But again, the supine GOP have fallen in behind him, two officers who were injured trying to defend the Capital were booed by Republicans when they appeared before Pennsylvania's House of Representatives. The rot has well and truly set in. — Wayfarer

You know how this goes. I did not come here to out-talking-point anyone. I'll see your "two officers who were injured" and raise you an Ashli Babbitt. I daresay if a white cop had shot a black woman to death for no particular reason, and the cop skated without even an investigation, certain members of society would be burning down buildings.

I truly have no interest in debating J6. It was a protest that got out of hand. Many of the protesters were peacefully escorted into the building by the capitol police. Trump's prior request for the National Guard was turned down by Bowser and Pelosi. It was a setup. The hysteria that the Dems made out of the incident is a Reichstag fire for our times.

I watched the left destroy cities, get slaps on the wrist for throwing molotov cocktails into police cars, and set fire to police stations with cops inside. The double standard is blatant.

I hear Steve Bannon's going to prison for contempt of Congress. Eric Holder didn't. Why is that?

The politically biased application of the law is far more concerning than the prospect of a second Trump presidency.

I'll agree wholeheartedly that the GOP are supine. Trump is not a Republican. He's commandeered the party for his own purposes. The regular GOPs hate him and can't wait till they get their ineffectual and depressing party back after he's gone.

I did not come here to defend the merits of Trump. I asked if you would cut down the law to get at the Devil. Many on the left say yes. I think you will rue the day.

ps -- This just came across the wire. AG Garland will defy Congressional subpoenas at his whim. I assume you'll support his imprisonment.

https://twitter.com/cspan/status/1798007391801262179

Yes, of course you are right. It is no more help than saying that a table is an object. I was trying to re-instate the line between, let us say, a mathematical reality and a physical reality - or between mathematical possibility and physical possibility. (I think we are agreed that what creates the difficulties here is the confusion of the two in the definition of the supertask.) — Ludwig V

I think there are abstract things and concrete things. But physics these days pushes hard on the nature of physical things. Is there a philosopher in the house?

I'll do better. I retract much of what I said of Searle — noAxioms

You know, Searle got into some trouble a while back, he was harassing the female grad students. A lot of other Berkeley philosophers knew about it and looked the other way because Searle is a Great Man and brings great prestige to the department. Caused quite a stir a while back. He had his emeritus status revoked. So goes academic politics.

I read the transcript of his Ted talk, and yes, he seems to attempt to stay physical. — noAxioms

Good, maybe I didn't misremember that.

I perhaps have mixed up some assertions from Chalmers, It is Chalmers that needs to explain how the arm goes up, not Searle, who seems to have a consistent story about this. — noAxioms

As I recall it, Searle said it's a great mystery why his arm goes up after he wills it to. So that's the opposite. How does Searle say it goes up in the TED transcript?

The Ted talk seemed to play the language game. If two things are doing the exact same thing, it is 'X' if a human does it, and it is not X if a machine does it. That's what I got from it. — noAxioms

Yes I can see that. When Xi Jinping speaks Chinese, he understands Chinese. When the Chinese room speaks Chinese, it doesn't. I can see why people throw rocks at Searle's argumen. When you state it that way, it's hard to defend.

I got nothing from him that suggests that human consciousness cannot be simulated, that it isn't computational. That bit seems to be your assertion. — noAxioms

Searle doesn't appear to know much about computation, and certainly didn't when he first made the Chinese room argument. To be fair, nobody did back then. But his room operates by a big set of deterministic rules, so I assume he would mean computability if he had known about it back then.

My apologies if I seem to respond to most of your comments. We both tend to do that, which makes the replies lengthy. I try to edit out repetitive replies. — noAxioms

Yes thanks. We both want this shorter and both collude to make it longer.

Consciousness is physical but not computational.
Why do you want this to be the case? It doesn't seem to be just a random assertion. — noAxioms

Because I can't believe that a computer program of any complexity, running at any speed, could ever be conscious. Euclid's algorithm computes the least common divisor of two integers. I can't imagine that running it fast enough would suddenly make it care.

I reject many of the common arguments. "Brains are made of neurons and graphs with weighted nodes are just like brains with neurons." Rejected. The nervous system is much more complex than that, and we don't know how it works. "We process information, computers process information, same difference." Rejected. Equivocating information processing. "Programs exhibit emergent behavior (I accept that) and consciousness is an emergent behavior." Rejected, because consciousness is not a behavior.

I see so much specious logic among the cognitive cognoscenti. (I just made up that phrase!) The bigger the intellectual cele
brity, the more vapid the logic outside their field of professional competence. George Smoot again. Great cosmologist. Lousy philosopher.

LOTS of things are physical but not computational.
I've said as much, but it doesn't prevent the running of simulations of parts of the universe. — noAxioms

Simulation as approximation. I can simulate gravity, I can simulate a brain. Not same as creating consciousness.

Why can all the other parts be simulated, but a human cannot? — noAxioms

Programs play chess and drive cars, and I'm duly impressed. Not same as being conscious.

I didn't say that certain aspects of human behavior can't be simulated. The chess programs are far better than the best human players these days. I know that. Desn't alter my point. Only makes it harder to defend :-)

It's not like the simulated human has a different reality to compare, and say "Hey, this consciousness feels different than a genuine consciousness does!". Maybe it 'feels' totally different from one person to the next, and not just from one universe to the next. — noAxioms

What is a simulated consciousness? As in an approximated or artificial consciousness. If we could make a conscious machine, I'd be amazed, but many believe they are working on it.

None of it is about proof. But a shred of evidence always helps. — noAxioms

I have arguments, not evidence. What would constitute evidence of what might be possible in the future? The ultimate argument against my position is that some configurations of atoms are self-aware, and someday we may figure out what those configurations are. I have no counterargument. I'm afraid it might be true. In the end maybe I'm just a geocentrist threatened by the revelations of Copernicus and Galileo.

I have no proof that the universe isn't computational, but the evidence suggests that. If we're 'in a sim', the sim has to go out of its way to fake that evidence. Bostrom addresses this problem. — noAxioms

For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together.{i] -- Colossians 1:15-17. Sim theory is theology. Christian theology at that.

You seem to think I assert this, or even that it's my opinion. It isn't. Evidence suggests otherwise. There's no proof either way. — noAxioms

My misunderstanding. This referred to the claim that everything physical is computational. If you agree with me that you don't assert this, then we're in complete agreement. In fact I think we might be in a lot of agreement in general.

OK, so we're back to zero evidence for your opinion, which doesn't make the opinion wrong, but it also isn't evidence against the SH. It only renders SH something you won't believe because it conflicts with your opinion. — noAxioms

I don't think I've denied that. You are correct. I have an opinion. No evidence.

That's where we differ. I don't reject something because of conflicts with my opinions. I don't consider my opinion to count as evidence one way or another. — noAxioms

I have my beliefs, but I could be wrong.

Perhaps there is something about life. We don't know what life is. Why do some arrangements of atoms become alive? And when we die, we're the same atoms. Soul, life energy. Consciousness is connected to those things. Programs don't have souls, don't have life energy, aren't alive.

Science is not about proof. I've always agreed with you on this point. Evidence suggests physics is noncomputatinal, and a rolling rock (a genuine one, not a simple approximation of one) is physics. — noAxioms

You are completely agreeing with me I think.

Yea, but my opinion doesn't count, except that my opinion rejects Bostrom's probability argued to the first two options. — noAxioms

I think we're pretty much in agreement on everything by now. Except Bostrom's meaning of simulation.

And my point is that like the rolling rock, it being noncomputational doesn't prevent it from being simulated to enough precision that it works. — noAxioms

Of course. Agreed. But "works" is relative. Like dark matter. Our theory of gravity works, but we know it's not quite right.

There's no evidence that consciousness is dependent on non-computability. If it was, then indeed, it could not be simulated at all. The lack of evidence of this dependency means that the SH isn't falsified by this [lack of] evidence. Falsification requires evidence. — noAxioms

I already agree.

Yes, you got it. Functioning in a computational way means being approximated to sufficient precision. I can approximate a car crash to sufficient detail that when I finally make a genuine car, I will know how safe it is, how it handles specific collision scenarios. — noAxioms

Well just about anything can be approximated to sufficient precision. I agree with that.

Except for consciousness. And perhaps life. The deep mysteries.

Note that I am using here and earlier the word 'genuine' as defined by Ludwig at the top of this post, since his definition of 'real' would not be fitting. — noAxioms

Not sure I recall the def.

OK, I grant that. I just want to know if the rock will bust in two when it hits that other rock, or if it will essentially bounce off with only small fragments ejecting. I don't expect the simulation to predict exactly which atoms within it will decay during the time simulated. No amount of precision will predict that. — noAxioms

Right. But the universe does it anyway. How does the universe know exactly how things will work, and not just approximately? Well, I don't know. I suspect it might not be computational. We should at least consider the possibility.

Those we can predict with enough precision, with enough detail of initial state. — noAxioms

Oh no, that's chaos theory. Even if we had all the details of the initial state, we can't necessarily predict the future. Tiny rounding errors add up to great differences in output. Nearby points in the initial state space lead to vastly different outcomes. We know this. Even totally deterministic systems can't be arbitrarily predicted.

Those are classical properties. They do have simulations of dark matter, and they explain the unusual rotation curves of some galaxies. — noAxioms

Is that right? Forgive my astronomy error. It doesn't invalidate the point I was trying to make.

The simulations show how those galaxies seem to have little dark matter in them compared to most. The simulations don't get the predictions correct partly due to the inability to guess correctly at initial conditions. Bostrom doesn't seem to address this problem in his paper. It is apparently 'hand waved' away. How does one set up initial conditions of this 'ancestor simulation'? Apparently an exercise for the people of the future to solve, — noAxioms

Ok. I better go watch some more Sabine, she's very good on dark matter and MOND.

Another good point about the ancestor simulations. How do they handle chaos? Slight differences in initial conditions plus rounding errors in the hardware (assumed digital, so essentially like our own computers, just more powerful).

He explicitly assumes that the "simulation" implements consciousness.
Yes, he does. This point obviously grates against your opinion enough to prevent further reading. — noAxioms

Well you've motivated me to slog through some more. But this does actually answer a question I've had for a long time. I wasn't sure if Bostrom just meant our experiences are simulated (like an immersive video game) versus our minds actually being created in the computer. He means the latter, explicitly.

Yes, that's what he's talking about. I thought that was clear, even from the abstract. — noAxioms

Not to me before I finally read it closely enough.

He does not suggest that we're computer programs. — noAxioms

That's exactly what he does suggest! He says that in the future, computations will instantiate consciousness.

Being a program is very different than being simulated by one. — noAxioms

Oh my ... not sure I know what that means.

You don't buy the hypothesis because it conflicts with your beliefs. Nothing wrong with that. — noAxioms

Right. I don't think a Turing machine will ever be conscious. Turing himself made that point. He said (in his 1950 paper on machine intelligence) that we can never know if a machine is conscious. We can only look at behavior, hence his Turing test. We can only observe behavior.

I hate to say it, but how does instantiation differ from execution of a model? I thought I had got it right, but now you're treating these terms as distinct. — noAxioms

Very distinct. The universe, or God, instantiates all the stuff around us. It is the stuff around us. It's the exact ultimate laws of the universe. The execution of a model is just that. It lets us predict, to sufficient accuracy, how the galaxies will move. It doesn't move the galaxies and it's not exact.

God or whatever creates gravity. We can make computer simulations of gravity by executing programs that implement abstract (ie approximate or incomplete) models of gravity.

To me the distinction is clear. Instantiation is the territory. Execution of a model is the map. The map is not the territory.

No, but simulated bowling balls are attracted to each other (not much). — noAxioms

They are not. The simulation can spit out a number that tells you how fast the bowling balls would move towards each other if they were real. But there aren't any bowling balls being moved. Only a computer model.

Either that or the gravity simulation isn't as accurate to sufficient precision. Most gravity simulations don't go to that precision. — noAxioms

Nothing to do with precision. Gravity simulations do not attract nearby bowling balls. They do not instantiate gravity.

Does that help with the distinction? We can simulate gravity but we can't instantiate it. It's already been instantiated by causes that we can't fathom. I hear that mass is the binding energy inside the quarks, and that mass distorts spacetime; but that doesn't actually tell us how it all came to be.

Oh dear this got long again.

fishfry will speak for himself. But I think the point is that, even a convergent sequence, which does have a limit, does not have a end or last step defined - indeed, is defined as not having one. That means that any answer whatever is equally valid and invalid. — Ludwig V

You totally get it. @Michael's turn :-)

I'm really tempted to respond to all your latest comments, but you're getting impatient, so I'll hold back and move forward. — keystone

This isn't going anywhere. And as I've mentioned, the real numbers are categorical[/math]. That means that up to isomorphism, there is only one model of the real numbers. If you have a construction of the real numbers, it produces the same real numbers as anyone else's construction.

So I will stipulate that you have a construction of the real numbers (though I don't think you do). But then, so what? I keep asking you that. You have an alternate construction of the real numbers. But whatever you have constructed is exactly the same thing as the regular old real numbers.

Just like you can use Dedekind cuts or Cauchy sequences. You can have a preference for one or the other, but it makes no difference.

In later posts, I aim to demonstrate that calculus not only remains intact with my perspective, but is actually built on firmer foundations. However, before we advance I'm going summarize the essentials so far. If you understand what I'm saying (even if you don't agree) we'll be ready to proceed. — keystone

Well if you have the intermediate value theorem and the least upper bound property -- ie, completeness -- then what you have, whatever it is, is isomorphic to the standard real numbers. Perhaps you have better philosophy, or a story you find more satisfying. But logicians have shown that the real numbers are categorical. There aren't any alternate models.

1) Initial Composition: My line consists of the same points and numbers as the real line. However, initially, the continuous points bundle together to form a line, and the continuous numbers bundle together to form an interval. Thus, we begin with a single object (a line) described by a single interval.

2) Isolation Through Cuts: A point/number can only be isolated from the line through a cut. Until the cut is executed, it is meaningless to refer to the point/number as an independent entity.

3) Rational Cuts: A rational cut corresponds to isolating a rational by bisecting the line.

4) Irrational Computable Cuts: An irrational computable cut corresponds to a non-halting algorithm that isolates an irrational computable within an arbitrarily small interval. This cut cannot be executed completely.

5) Irrational Non-Computable Cuts: These cuts don't exist. Irrational non-computables cannot be isolated.

6) Completeness: All the points are there from the start (bundled in the line) so in a sense the line is complete. However, it is impossible to fully cut the line such that all points/numbers are isolated so in a sense the isolated points/numbers are incomplete.[/qouote]

Without disputing point by point (for example, you're wrong about noncomputables, because if you don't have the noncomputables, you can't have completeness), it doesn't matter. If you have the real numbers, they're the same real numbers.

And your claim of completeness but no noncomputables is inconsistent. One of those has to go.
— keystone

PLEASE try to understand the following example (including the figures!). This is essential for me to make any progress explaining why calculus doesn't collapse with my view. — keystone

No, I don't need to. If calculus works, then you have the standard real numbers.

Perhaps you are building the constructive or intuitionistic real line. Did I already mention those earlier? If so, they have a theory of computable completeness that lets them finesse the issue. Perhaps you mean that.

Notice that in these 1D examples the figures contain the same information as the unions. It contains no additional information, but when we move to 2D, the figures become much more significant. — keystone

Skipping the next bits ...

π is the familiar irrational number and ε1 and ε2 are arbitrarily small positive numbers. — keystone

No such thing as an arbitrarily small positive real number. Not in the standard reals, not in the constructive reals, and not in the hypereals. That's because if epsilon is a positive real number, then

0 < epsilon/2 < epsilon.

It's essential that you understand that. The real numbers are a field. You can ALWAYS divide by 2.

Their independent values are not important as they are never used in isolation. What's important is that π-ε1 and π+ε2 are rational numbers and π lies within the arbitrarily narrow interval (π-ε1,π+ε2). — keystone

There is no such thing as an "arbitrarily narrow interval." I believe I've identified the exact flaw in your thinking.

Do you follow what I'm saying? — keystone

I think I've refuted it. Two points to sum up:

1) The real numbers are categorical. Any two models are isomorphic; and

2) There is no such thing as an arbitrarily small positive real. That's because the real numbers are a field, in which you can always divide by 2.

I'm afraid there was a typo in my last post. I posted "Infinity is certainly not a concept", which is rubbish. I meant to post "Infinity is certainly a concept". Apologies. — Ludwig V

In online discussions of infinity, someone is bound to come along and say, "Infinity is a concept." Which always makes me say, So What? 3 is a concept. 47 is a concept. Civilization is a concept. The rules of the road on the highway are a concept. Saying infinity is a concept doesn't actually tell us anything about it. I don't even know what it means to say infinity is a concept. Is there anything that isn't a concept?

Yes, I realized that and was hoping to produce a formulation that would allow a more constructive discussion. — Ludwig V

I gave it my best shot just now. cc @Michael

I have always agreed that the sequence "0, 1, 0, 1, ..." does not converge. — Michael

Ok. Agreement is good. I appreciate that.

I hope you agree that building a mathematical model of the problem is a valid way to approach it.

I do recognize that "a supertask is not just an infinite sequence," as you've often told me. I agree with that too.

But if you will accept that "0, 1, 0, 1, ..." does not converge," I can work with that for a start.

I disagree with your claim that with respect to Thomson's lamp we can simply stipulate that the lamp is on after two minutes. — Michael

I get that. That's where we disagree. I'll try to clarify my argument the best I can.

See my previous post and my initial defence of Thomson on page 13. — Michael

Coming up ... at least just your previous post, not necessarily going back through the thread. This is page 24, that's a long time ago. Is there something I should see in there that you haven't said recently?

Okm to your previous post.

A supertask is not simply an infinite sequence of numbers. — Michael

I agree with that.

In our hypothetical scenario with hypothetical physical laws we are still dealing with the ordinary logic of cause and effect. — Michael

I understand your point of view. But here is no cause and effect between the oscillating lamp sequence, and its arbitrarily defined terminal state.

It is implicit in the thought experiment that it is only by pushing the button that the lamp is caused to turn on and off, but strictly speaking this premise isn't necessary as the logic applies regardless of the cause – even if it's magic. — Michael

Ok, fine. I'll work with you on that. Let me replace your earlier 60-second model with a 1-second model. That is, there's a final time -- let's call it midnight, in homage to Cinderella's coach. Let's say the light is on at midnight minus 1 second; off at midnight minus 1/2 second; on at midnight minus 1/4 second.

In general, it's on at $\text{midnight} - \frac{1}{2^{n}}$ when n is even, and off when n is odd, for n = 0, 1, 2, 3, ... That is, the lamp is on at the even-exponent inverse powers of 2, and off at the odd-exponent inverse powers of two.

So we have an easy way to know if the lamp is on or off. For example, what is the lamp state at midnight minus 1/128 seconds? Well, 128 is 2 to the 7th power, and 7 is odd, so the lamp is off. So far so good I hope.

If the lamp is on then something caused it to turn on, prior to which it was off. If it is turned on then it stays on until something causes it to turn off. — Michael

Well no, this is exactly the spot where you're wrong. Or being more charitable, the spot at which we disagree.

The mathematical model that we've just agreed to (assuming you agree with my notation) defines the state of the lamp at every inverse power of two seconds before midnight.

Say I claim the lamp is on at midnight. If you pick some earlier point, we can determine if the lamp is on or off.

But so what?

Two things are true: The lamp state follows the rule we've given; and the lamp is on at midnight.

That's perfectly fine. There is no contradiction I think you should be much more clear that you think that's impossible.

Likewise, the state at midnight could be off. That too, is perfectly consistent with our lamp state algorithm that works for any point BEFORE midnight.

Given this, if the lamp is on at t1 then either:

a) it was turned and left on prior to t1, or
b) it was turned and left off prior to t1 and then turned on at t1 — Michael

No it's never "left off" or "left on" prior to midnight. Whatever is its state at $\frac{1}{2^n}$ before midnight, it will have the opposite state at $\frac{1}{2^{n+1}}$ before midnight.

None of that has any bearing whatsoever on the terminal state, which can be anything we like, because, since the on/off sequence has no limit, there is no natural final state.

This "leaving on" or "leaving off" idea is not founded on anything. It doesn't even make sense. It's a consequence of failing to think clearly about the problem.

But as Thomson says, "I did not ever turn it on without at once turning it off ... [and] I never turned it off without at once turning it on", and so both (a) and (b) are false. — Michael

So what?

Therefore the lamp is not on at t1. Similar reasoning shows that the lamp is not off at t1 either. — Michael

On the contrary. I just showed that it's perfectly sensible for it to be on OR off. Either way is consistent with what's come before; and neither is to be preferred.

I hope you can come even a little ways toward my view. Before midnight, it's an infinite sequence. It has no end. It's never left on or left off. Whatever state it's in, it flips state at the next inverse power of 2.

The basic confusion is not understanding that an infinite sequence has no end. The state at midnight is arbitrary and is not related to what's come before, even under your pretend physics.

Thankfully, ↪fishfry is there to help guide you. — jgill

No good deed goes unpunished :-)

There are two cases in play at the moment - "0, 1, 0, 1, ..." and "1/2, 1/4, 1/8, 1/16.." Comments switch between them without always being clear. You are, however, quite right that the first sequence doesn't have a limit and the second one has what we could call a natural limit. — Ludwig V

I know I'm right :-) Now if I can just get @Michael to agree!

I want to make it clear that a line cannot be constructed from/defined by infinite isolated points (numbers) or micro-lines (intervals). If that's clear then what is a line --> — keystone

The real line is the set of real numbers. That's the modern view. Or as Euclid said, "A line is breadthless length."

Yes! Forget about declaring that the line is infinite individual things and instead call it ONE thing, ONE bundle, described by ONE interval. This is an important distinction because it frees us from actual infinity allowing for a stronger foundation. — keystone

Ok. One thing.

I can't do what? How small do you want the bundles to be? I assure you, I can divide them as small as you wish. Of course, I can never cut a line down to indivisible bundles, but I never claimed I could. Why would we even need that? — keystone

I don't know. Why is any of this important? You claim you can get to every real number via cuts, but only finitely or countably many of them. And that's not true. And the reason we need it is so we can have the real numbers.

You're right that I can't execute a cut to isolate an irrational point. However, what I can do is develop an algorithm that defines an endless cutting of the line such that the line segment containing the desired irrational point gets arbitrarily small. — keystone

You could not do that, for the reason that there are only countably many algorithms, and uncountably many irrationals. You haven't got enough algorithms.

As we've agreed, that algorithm is the irrational. There's no need to declare that the algorithm can be run to completion to output an irrational number. — keystone

There aren't enough algorithms to define all the reals. Most reals are noncomputable.

The algorithm is sufficient in and of itself. And if I need a number, I can interrupt the algorithm to deliver an arbitrarily narrow interval with rational end-points and I can pick a suitably close rational number within that interval. — keystone

Actually that is untrue. There aren't enough algorithms.

Now, I can't isolate a non-computable this way, but that's not a problem. The non-computable points are not missing from my view. They are included - my line is continuous. The non-computable points just cannot be isolated. But we don't need to isolate them. They fulfill their job being constrained to bundles. Do they not? — keystone

Well, if you want to see it that way, I suppose so. But without the noncomputables, the real line is not continuous. So they are there but they're not there?

I ask again: Suppose instead of endlessly sniping at your ideas, I just agree. What then? What is the point of all this?

My argument is that we don't need completeness. — keystone

Well then the intermediate value theorem is false. Calculus would collapse.

Let's embrace our inability to fully execute a non-halting program. Our inability to isolate everything is a feature of my view, not a flaw. After all, why do you need 2ℵ0
2
ℵ
0
isolated numbers? — keystone

They'e not isolated, I've explained that several times. But we need them for completeness! The completeness of the real numbers is the defining property of the real numbers. Without completeness they're not the real numbers.

Let's lay out all countably infinite rationals in an ordered line. How many gaps are there - countably many? — keystone

Uncountably many. Each gap represents an irrational.

What is the difference between a gap and a Dedekind cut? — keystone

A Dedekind cut is a pair of sets of rationals. A gap is a non-rational point. They amount to the same thing, expressed differently.

If they are the same, how do we arrive at uncountably many cuts? — keystone

Because there are uncountably many reals and only countably many rationals.

The answer is that Dedekind doesn't ever execute the cut. Dedekind Cuts only make sense if they correspond to non-halting algorithms which by definition cannot be executed completely. — keystone

That's just nonsense. It's wrong. But again, what is the end game of all this? Suppose I stop objecting and ask you, what is the point? Actually I have asked you several times recently.

I had asked whether you understood what I was saying and you said you literally have no idea. It's hard to move forward if nothing I'm saying is coming through. — keystone

Well you've made progress. You did say something I understand, namely that Dedekind cuts must correspond to non-halting algorithms. The problem is that it's utterly false. It's just a massive misunderstanding on your part.

Ha. My view has points, they're just not fundamental. Points emerge when a cut is made, but the line doesn't come precut and nobody could ever completely cut a line. — keystone

Ok. Fine. Now what?

The lamp is on only if the button was pushed to turn it on, prior to which the lamp was off. — Michael

According to what principle of physics?

If the lamp can violate the known laws of physics, what are the limits of its magic?

Or, if you want to introduce magic, it is on only if magic turned it on, prior to which the lamp was off. — Michael

But I didn't. YOU (and Thompson, who attained his terminal state in 1984 and is now enjoying his spaghetti) introduced magic. I'm just playing by your rules.

So if you want to say that the lamp was on after two minutes then you must accept that at some final time prior to two minutes the lamp was (left) off. — Michael

Not at all. I've given many counterexamples. The sequence 0, 1, 0, 1, ... has no limit. If I define its terminal state (that is, its value at the point at infinity) as 47, that's perfectly legal. And as sensible as any other terminal state.

The supertask doesn't allow for this. — Michael

Of course it does, and I have repeatedly explained how.

I really need a quote on that for context. — noAxioms

I have stipulated that I am not quoting Searle; but rather quoting my memory of what I understood of something he said in a video I watched several years ago. I could have misremembered, misunderstood at the time, or both. Clearly there is no hope of my finding the quote unless I go searching for Searle videos.

Can we just start from what I also said, that I am willing to make this maxim my own. Consciousness is physical but not computational. Now I have said that, and I believe it (obviously without proof), and the quote is right there. So we can discuss that, I hope.

He asserts that mind works differently than everything else physical. — noAxioms

Forget Searle. I'll own the position myself. And what you said is clearly wrong. LOTS of things are physical but not computational. The universe, for example. I have no proof of that either, nor do you have proof that the universe is computational.

If you have proof that everything physical is computational, feel free to post it, link it, or publish it. Or just admit it's your opinion. That's all anyone can have regarding these matters, till someone makes a heck of a scientific breakthrough.

Sounds like dualism to me. If it can be show that it really works that way, then physics needs to be rewritten to include this magic as part of naturalism. — noAxioms

Now that, I do not understand. We have a deep understanding of the limits of computation. Why do you think that anything non-computational must be spiritual or non-physical? You have no proof of that.

And how has this been demonstrated? — noAxioms

There is no demonstration of the proposition or its negation.

He has no more evidence of that than the science community has that it IS computational, but even a rock rolling down a hill hasn't been shown to be computational. — noAxioms

Wait, now you're agreeing with me. If a rock rolling down a hill hasn't been shown to be computational, then you admit that you claim that "everything physical is computational" has no proof.

So we each have an opinion, and nobody has a proof. I hope we can agree on that.

Point is, it's no big claim to say something isn't computational. — noAxioms

You have gone a long way towards agreeing with me. If a rock rolling downhill might not be computational, then surely consciousness might not be either.

The big claim is one that says that the effect in question cannot function in a computational way. — noAxioms

You seem to be making a distinction between "computaional" and "functioning in a computational way." I do not understand that distinction. Unless by "functioning in a computational way" you mean something that can be approximated or simulated by an abstract model. But that is not functioning that way -- it's only being approximated that way.

I assume you agree.

I can computationally simulate an approximation of the rock rolling down the hill, a simulation that will yield almost any property I want of a rolling rock. — noAxioms

I agreed with you right up till you said, "any property I want." Clearly we can't do that, because we haven't got a theory of quantum gravity, meaning that we have not yet got a complete theory of gravity. So there are SOME properties, tiny little wobbles, that we can NOT simulate or approximate, because we haven't got enough physics. Dark matter is a good example. Our greatest and most precise computer simulations of gravity can't get the predictions right, because we haven't yet got a good theory.

Bostrom's hypothesis suffers from this. A simulation seems necessarily classical, and yet science has demonstrated (Bell's theorem for starters) that our physics isn't classical. So Bostrom has to modify his hypothesis to change physics when attention is paid to it, to make it appear non-classical when in fact it actually is. That make the job of the simulation so very much more difficult. — noAxioms

Having read enough of the first page of the paper to throw it down in annoyance again, I think you are wrong about what he says.

He explicitly assumes that the "simulation" implements consciousness. How this happens he has no idea, but he assures us that this is "widely believed." By the TED talkers he hangs out with, I'm sure. By me, not so much.

So he is (in my reading) NOT talking about simulation as approximation; or simulation as a perfect implementation of an abstract model that captures most but not all of a system's behaviors. He is talking about my consciousness, this noisy voice in my head and the feeling of the keys under my fingertips, the pleasant sensation of the soft breeze coming in the open window, being literally implemented, instantiated, created by the "simulation." I find that most unlikely, for the simple reason that I don't think computer programs have inner lives. Of course I'm just saying I don't believe it because I don't believe it, so I haven't convinced anyone.

So he is using the word simulation to mean instantiation or creation; and NOT approximation or execution of an abstract model. I believe that. I will go back to the paper and read a little more and see if I can either find more ammo or perhaps a refutation of my belief. But as it stands, I reiterate that what Bostrom means by simulation, he should call instantiation or creation, so as not to confuse it with a simulation of gravity, which is an instantiation of an abstract model and not the real thing.

Remember: Simulations of gravity do not attract nearby bowling balls. I hope you will consider this.

As a sickly child, when I felt ill, I would imagine myself as heroically fighting severe illnesses, attributing my survival to extraordinary strength. Turns out, I'm just wimp. I was probably just dealing with a common cold last week. Fortunately I wasn't in tune with any of the bird flu news...anxiety doesn't usually help... — keystone

That's why the Amish communities weren't hit hard by covid. They don't watch tv :-)

Correct, but why does that matter? (0,1) is already the disjoint union of open intervals, namely itself.
— fishfry

The issue revolves around whether the part or the whole is primary. — keystone

How is that issue resolved by the question of whether you can partition the open unit interval into countably infinite many pairwise disjoint open intervals? You can't, but it certainly is the pairwise disjoint union of ONE interval, and so what?

If parts precede the whole, then logically, I should be able to union such parts to create the whole, which you acknowledge is not feasible. — keystone

I already showed you a non-disjoint countably infinite union of open intervals that equals the open unit interval. And the interval is the disjoint union of its uncountably many points. How many decompositions do you want? Why do you insist on the one decomposition that we can't do?

Conversely, if the whole precedes the parts, then I should be capable of bisecting the whole into smaller sections, continuing to do so until I have arbitrarily small parts. This approach is feasible. — keystone

You surely can't do that with countably many cuts.

Yes, individual points are entirely synonmymous with numbers. However, continuous bundles of points are synonymous with intervals. And what I'm saying is that it's these continuous bundles of points (described using intervals) that are fundamental, not the individual points (described using numbers). We start with a continuous bundle of points (described using an interval) and when we cut it (ie. bisect this interval), we not only create smaller continuous bundles of points but also isolate an individual point in between (described using a number). Hence, the individual points and their associated numbers emerge from the bisecting process; they do not exist as independent objects before it. Individual numbers and points are emergent. — keystone

I asked you earlier: Suppose that rather than snipe line by line at this paragraph, I just accept it for sake of discussion. Can we move forward? I just don't see how any of this matters. And your bisection idea doesn't work, you can't get any irrationals that way. But I believe you've already agreed with that.

When I presented that table and you wrote 'I would have to give this some thought' but didn't follow up on it, is it that you don't want to consider an alternate view? — keystone

I found


The common theme throughout all of my posts (including this one) and summarized in that table is that I believe we must start with the whole and manipulate it to produce the parts. Building (or defining) the whole from the parts is hopeless. Do you understand what I mean by this?[/quote]

I found the fitness gym analogy confusing and pointless. But of course your whole approach is pointless (that's a pun) so maybe I'm getting it.

When it comes to the real numbers, I do think building the parts from the whole is difficult, because you'd need uncountably many cuts. But Dedekind has already built the reals from cuts of rationals, so it can be done. But there are uncountably many cuts.

I think that there some rules that apply in fiction (imaginary stories), because the story needs to have plausibility. But I don't know how to work out what they are. Coleridge, I think it was, said that there needs to be a "suspension of disbelief" for any fiction to work. The reader/audience needs to co-operate and not ask awkward questions. But there are limits. There needs to be some realism for the story to be recognizable at all. — Ludwig V

You've solved my problem. I need the willing suspension of disbelief to converse with @Michael. Indeed, that's the question I asked him. What's the difference between Thompson's lamp and Cinderella's coach? Why am I supposed to treat the lamp as if it has a button, or is operated by a computer program (that likewise can wait for arbitrarily small time intervals), or is subject to some rules of rationality but not others?

I would gladly put these questions to Thompson, but Wiki says he died in 1984. I dare say that if there's an afterlife, he is now eating his plate of spaghetti.

Another boring “both-sides” guy. How original— how interesting. — Mikie

That's funny. The other day you accused me of getting my world view from Sean Hannity. Today you're crediting me with openmindedness. I suppose that's an improvement.

Actually if you read my post, I get my world view on this issue from A Man for All Seasons. I'd give the Devil the protection of the law for my own safety. A point that every single respondent has totally missed. @Wayfarer says, "I see what side you're on" as if I'd opened with partisanship. I went out of my way not to. J6! J6! J6! Complete with a picture. As if that bears on anything I said.

I must say, nothing in this thread has impressed me about the assembled philosophers. Is it the Lounge, or just the Trump effect? Logic, reason and reading comprehension are in short supply.

We stop at the single issue being discussed: performing some action at arbitrarily small intervals of time. So taking the code here we assume that each line is run in an instant with the exception of the wait i *= 0.5 line which waits for the specified time in seconds. The logic of the code still behaves exactly as we would expect. Thomson is asking us what is output when echo isLampOn runs. — Michael

Can you answer this question that I asked earlier? What is the difference in the ontological status between Thompson's lamp and Cinderella's coach?

If your only solution is to insert the line isLampOn = 'a plate of spaghetti' after while (true) { ... } and before echo isLampOn then you are not answering the question as posed. — Michael

But it's not my only solution. I've said (several times) that "Lamp is on" and "Lamp is off" are also valid solutions. Just about anything in the universe, physical, abstract, or fictional, is a valid solution.

After all the times I've explained this to you, I don't mind if you say, "You're wrong." But how on earth can you say that MY ONLY SOLUTION is X? I have already said that ANYTHING AT ALL can be a solution; and that if you insist that on/off are the only legal solutions, then either one is valid.

I don't mind having a difference of opinion, but you seem to have not read a single thing I've said.

If you cannot make sense of the echo isLampOn line without inserting some arbitrary code before it then you must accept that it doesn't make sense for while (true) { ... } to complete. The arbitrary code you are trying to insert is a smokescreen to disguise this impossibility, exactly like your magic turning the lamp into a plate of spaghetti. — Michael

You accuse ME of magic! YOU are the one with the lamp that switches state in arbitrarily small intervals of time. I'm playing by YOUR rules, which clearly allow magic.

Of course I have already made that point to you many times as well.

Ah, Searle said that, which makes sense. Of course Searle isn't going to accept a naturalist premise, but his unwillingness to set aside his opinion about it prevents his rendering any proper critique. — noAxioms

I totally don't get what you said.

Searle is making an entirely naturalist premise. He denied dualism. He says consciousness is physical, just not computational. How do you get from that, to "Searle isn't going to accept a naturalist premise?" He's insisting on a naturalist premise, isn't he?

Again I must emphasize that I am not claiming Searle made this point; only that I interpreted what he was saying as his making this point in a video I watched a couple of years ago. For all I know I made up the whole thing.

But whether or not it's Searle's point, it's my point. Consciousness is physical, but not computational. Penrose has argued the same point.

The opposite of computational is not superstition or dualism. It's that there is something else going on that is not computational, but still physical.

People keep using the word naturalism and I'm trying to understand what it means. Is it the same or different than physicalism?
— fishfry
For purposes of this discussion, I've been using the two terms interchangeably. — noAxioms

Ok thanks. So the view that I ascribe to Searle is naturalism. Don't know why you interpreted my explanation as the opposite.

Computationalism is not physicalism.

Penrose's view is described in his book, The Emperor's New Mind.

Wiki says:

Penrose argues that human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine, which includes a digital computer. Penrose hypothesizes that quantum mechanics plays an essential role in the understanding of human consciousness. The collapse of the quantum wavefunction is seen as playing an important role in brain function.

This may be a crackpot idea, but at least it's Sir Roger's crackpot idea. And as someone said, Sir Roger's bad ideas are better than most people's good ones.

Thanks! Mostly better now. — keystone

Not bird flu I hope. Jeez the medical propaganda is everywhere these days. Are we all doomed? Like not eventually, but as soon as next week?

Allow me to further clarify my position. I can write (0,1) as the union of arbitrarily many disjoint intervals. However, I cannot write (0,1) as the union of infinitely many disjoint intervals. — keystone

Correct, but why does that matter? (0,1) is already the disjoint union of open intervals, namely itself.

Do you think you understand my position so far (and perhaps don't agree with it) or do you have no clue what I'm proposing? — keystone

I literally have no idea what we've been talking about the past several weeks. Which makes me feel foolish sniping at it.

I don't have an alternate way of getting to the real numbers. What I lay claim to is the real points, not the real numbers. — keystone

But points and numbers are entirely synonymous in this context. The "real line" is just the set of mathematical real numbers.

Consider the ruler depicted below. — keystone

Your diagrams make my eyes glaze. I appreciate that they're meaningful to you. They are not helpful in terms of communicating with me.

It features 96 tick marks
... — keystone

Eyes glazed. I'm sorry. I feel terrible because you put so much work into these diagrams.

You actually lost me when you distinguished between the real numbers and points; since as far as I know, they are the same thing.

The fact that the length of each line in your sequence is getting shorter is a red herring. Every single line in your sequence is composed of exactly 2ℵ0
2
ℵ
0
points. The point count isn't converging to 1. What you've exhibited is not actually a nested collection of lines but an algorithm for generating such a collection (or at least the essence of an algorithm). This distinction is crucial because the algorithm, if executed, doesn't halt. If you chose to execute the algorithm, the best you can do is wait for a long time and interrupt it when the last line produced is sufficiently small. In other words, the output of the algorithm is an arbitrarily small line, not a point. — keystone

Actually algorithms are not relevant, because I need not have a finite description for the set of open intervals that descend to a point. It's not a computational process.

Do you believe individual rational numbers can be isolated? — keystone

Perhaps you are using a different definition of the word. Mathematically, no rational number is isolated, because every interval containing a given rational necessarily contains others.

But if you have some other definition, you might convince yourself otherwise.

I believe they can. I'm going to use the SB tree to illustrate my view, — keystone

Eyes glazing like a ham on Easter.

not because it's essential but because it's familiar. — keystone

This example is useful to you but it is not helpful to me.

I can cut this tree such that left of the cut is (0,1/2) and right of the cut is (1/2,inf). With this cut, I've isolated 1/2. I cannot do the same for irrational numbers. — keystone

If that's what you mean, then so be it.

I take the point. I may not have stated it accurately enough, but the crucial thing, it seemed to me, is to realize that the limit is part of the definition from the start - not, as I think you're saying, something that is worked out from the sequence itself. — Ludwig V

Yes, and now I hope I did not overstate my case. I'm making an abstract philosophical point. The main thing is that the terminal state (the state at the point at infinity) bears no necessary relationship to the sequence that precedes it. But if we are given a sequence that does happen to have a limit, we can generally determine what the limit is. I don't recall how we got started on this, but the lamp sequence doesn't have a limit so the terminal state has no natural answer.

A supertask is not simply an infinite sequence. — Michael

Understood.

With a supertask we are given some activity to perform and we assume that it is physically possible to perform this activity at successively halved intervals of time. We are then asked about the causal consequence of having done so. — Michael

The lamp is not physically possible. Supertasks are not physically possible per currently known physics. Surely we agree on these two things. Yes? No?

We do not get to introduce additional (and nonsensical) premises such as "and then the lamp magically turns into a plate of spaghetti, prior to which the lamp was neither on nor off." — Michael

Well this is exactly the point I'm making. Why do we get to introduce a nonsensical premise such as a lamp and a switching circuit that can change states in arbitrarily small intervals of time, in contravention of the principles of quantum physics and electrical engineering?

My point is that once we've entered the realm of speculative fantasy, where do we stop? I say the lamp switches in arbitrarily small intervals of time, AND turns into a plate of spaghetti.

And you say ... what? That it CAN violate some laws of physics, but CAN'T violate others? Why?

The lamp must be either on or off after two minutes. — Michael

Suppose that I accept this additional stipulation to the problem. Then I say it's on at two minutes. Or I say it's off at two minutes. Both are consistent with the premises of the problem; and neither is to be preferred, since neither are the limit of the sequence. You can make it anything you like. I use the spaghetti example to illustrate the arbitrary nature of any stipulated terminal state. One answer is as good as any other.

If the lamp is on after two minutes then it is on only because the button was pushed to turn it on, prior to which the lamp was off. — Michael

Now you (and Thompson) are trying to reason logically about a hypothetical situation that is entirely fictional, namely a lamp that switches in arbitrarily small intervals of time. You accept that, and then try to flim-flam readers by appealing to readers' experience with actual lamps.

But the Thompson lamp is not an actual lamp! So you can not reason about it as if it were the lamp in your living room. There is no button, there is no bulb, there is no electric bill to be paid at the end of the month. There is only an entirely fictional situation that you are pretending to reason about as if it weren't entirely fictional.

If the lamp is off after two minutes then it is off only because the button was pushed to turn it off, prior to which the lamp was on. — Michael

No. Not so. The terminal state of the lamp has nothing at all to do with what has come before. It's just like the mathematical sequence 0, 1, 0, 1, ..., to which I arbitrarily assign a terminal state (a state at the point at infinity) of 47. It's arbitrary. It's legal. It violates no laws of God or man.

The supertask doesn’t allow for either of these scenarios and so is proven impossible in principle. — Michael

You are as wrong as can be. I have explained this to you muliple times.

It's not a real lamp. It is not constrained to buttons and it's not plugged into a wall and connected to the electric company. It's a fiction.

Tell me this. Did Cinderella's coach turn into a pumpkin or not?

Do you not see that Thompson's lamp has the exact same ontological status as Cinderella's coach? It's a fairy tale. It's silly to try to reason as if it were a real thing, subject to the laws of this world.

But that's an issue that goes back millennia. A century ago, there was "elan vital" or "Life Force". Before that, it was the "mind", the "soul". Aristotle's "psyche",
Searle's mystery component can be seen in his Chinese Room. It is (from what you tell me and my memories) just a gesture towards something in the future. — Ludwig V

It's an intermediate position between physicalism and computationalism. Whether it's true or just superstition, we'll have to find out.

I'm sorry. It was lazy of me to do that.
One point about it was indeed that the physical basis of the emotions is clearly not just a matter of processing information. The focus on the brain, together with the computer analogy, misleads us. Even the knowledge that we already have should prevent us from thinking that there is necessarily any simple correlation between mental and physical phenomena. People equate fear and anger with the circulation of specific hormones. But that is, surely, clearly not the sort of thing that our computers can do. It is one phenomenon in among others that are associated with the emotions. The brain, presumably, is involved in triggering the release and the whole of the rest of the body is affected. Compare the call of "action stations" in a ship or perhaps the fire alarm in a building. Everything is affected. There's no way of picking out the specifics, except by the general description "ready for action" or "falling in love".
Computers of the kind we are familiar with do not (so far as I can see) have any capacity to be afraid or fall in love, to value one outcome over another and one of the reasons for that, it seems to me, is that the way they "think" has no conceptual space for those things. (Though I'm sure that some people will respond to the challenge by developing simulations.)
I'm going to stop there. There's not much I'm sure of beyond this point, except that philosophers don't seem to be able to grapple sensibly with what's going on here. — Ludwig V

I think you agreed with me and expressed my thoughts. If so, thanks!

Nobody on 'the left' was responsible for that day of infamy. — Wayfarer

Actually there's considerable evidence that people on the left were responsible; namely, Nancy Pelosi and Muriel Bowser, who denied Trump's request for the National Guard. And the J6 committee was a total politicized fraud.

But you are making my point. Trump was not on trial for J6, but you think he was. Or more accurately, you just don't care. You are Thomas More's prosecutors, willing to cut down the law to get the Devil. Many on the left simply can't see the bigger picture. You can have the last word. And in the end, history will.

There may be sharp criticisms from the left and right, but denying the result of elections — Wayfarer

But enough about Al Gore, Stacy Abrams, and Hillary Clinton.

By the way, Hillary committed the exact same crime. She paid for oppo research against Trump and wrote it down as legal expenses. She was fined over $100,000. Maybe you missed this story.

https://www.politico.com/news/2022/03/30/dnc-clinton-campaign-fine-dossier-spending-disclosure-00021910

Again, my point is not whether Orange Man bad. It's the unequal and politicized application of the law that even some on the left are deeply concerned about.

and attacking the rule of law — Wayfarer

It's the left on a rampage agains SCOTUS these days. Respect for the law seems selective, depending on whose ox is gored. Like when Schumer publicly threatened the Supremes. Didn't see much respect for the rule of law that day.

"I want to tell you, Gorsuch, I want to tell you, Kavanaugh, you have released the whirlwind and you will pay the price. You won't know what hit you if you go forward with these awful decisions."

I'm sure you objected to the (at the time) Senate Minority leader's attack on the rule of law that very day.

should be abhorrent to both. — Wayfarer

If you will reread my post (or read it for the first time, based on what you just wrote), you'll see that I said that one could loathe Trump yet share the concerns I raised. Liberal legal commentator Elie Honig and former Democratic Governor of New York David Patterson, among others, have expressed similar views recently.

@Paine, @Mr Bee, @T Clark, @Mikie, @Wayfarer, thank you for your replies.

I said my piece and have nothing to add. I'm content to let the future speak for itself. In the fullness of time, some opinions may change as the inevitable consequences play out. There are sharp criticisms of this prosecution from the left as well as the right, so I know I'm not alone in my view.

No, they are not just hormones. The causes of the hormones in the brain and the effects of the hormones in the body, together with their psychological counterparts are all part of the package. Think about it. — Ludwig V

I could think about it a lot, without ever figuring out what you were trying to tell me here!

I thought I was agreeing with you, that emotions are an argument against computationalism. But perhaps I misunderstood.

It makes no sense to answer this question with "a plate of spaghetti" or "1/2 — Michael

The 1/2 was Thompson's idea. The plate of spaghetti is mine, inspired by Cinderella's coach, another omega sequence paradox that's not usually recognized as one.

The thing you and Thompson keep missing is that the lamp is not real. It violates the currently known laws of physics; and because it stipulates a circuit that can change state in arbitrarily small intervals of time as modeled by the mathematical real numbers, it's difficult to imagine, even speculatively, that the lamp could ever be physically realized even under far future physics.

So there is no "logical" way to connect the sequence, with its arbitrary terminal state, which you can define as on or off. Or as a plate of spaghetti, if you so desire. There's nothing about the lamp that's real. The lamp can turn into a plate of spaghetti exactly as Cinderella's coach turns into a pumpkin. By fiat in a fairy tale.

Please see my response to @Ludwig V above, where I expand on this theme.

https://thephilosophyforum.com/discussion/comment/907876

I understand that. What seems important to me is that the convergent series is the result of a calculation which involves 0 and 1, while "0,1, 0, 1, ..." doesn't involve any calculation at all. You could also have a series "a, b, a, b, ..." or "fish, chips, fish, chips, ..." The calculation involves numbers, but "0, 1, 0, 1, ..." only involves numerals. — Ludwig V

Well, it's not a calculation. The limit, or the terminal value, is not necessarily the result of any logical process. I keep trying to explain this to @Michael. The limit of 0 does not "come from" the sequence 1/2, 1/4, 1/8, ... in the sense that you could put those numbers into a machine and 0 would pop out.

Rather, you are given the sequence; and given the limit; and you can apply a formal definition to see that 0 is indeed the limit of the sequence. It's conceptually sort of the other way 'round from thinking that the limit is the result of some logical process applied to the sequence. Although "find the limit of this sequence" is a common calculus problem, so there are heuristics and strategies to find limits of sequences that have closed-form representations. But not all sequences do, so my remark stands.

That's the think with the lamp. You can define the terminal state as on or off. Neither makes sense, and neither is forbidden. The sequence still stands on its own terms. On, off, on, off ... All that happens, as you count through 1, 2, 3, ... Then you arbitrarily assign a terminal state. On, off, or a plate of spaghetti.

@Michael just doesn't get this or just doesn't want to get this.

If Thompson were here I'd explain this to him. Thompson and @Micheal are making the same conceptual error. There is no logical relationship at all between a sequence, and some arbitrary terminal value. If the terminal value happens to be the formal limit of the sequence, that's a lovely special case that happens a lot in calculus class, where all the problems are designed to work out nicely for diligent students.

But it can't happen with the lamp. The sequence on, off, on, off ... does not have a limit

End of story as far as I'm concerned.

Do we have any inkling of how brains are conscious? — RogueAI

I don't. Science doesn't. But the computationalists, they are very sure of themselves. Consciousness is something that can be implemented by a computer program. And the arguments are specious. We process information, computers process information, therefore we're like computers. Weighted nodes in a graph are just like neurons. You can't argue with these people. They control TED, hence the popular "educated, sophisticated" mind. It's better to go along with what all the other cool kids say. Consciousness is computational, we're in a simulation, aren't we clever.

A lot of really smart people, too. Cognitive neuroscientists, rock star CEOs of AI companies. Who am I to argue?

Thanks for asking :-)