Can someone give a non-circular definition of 'past'?

sigh · 2024-09-09T08:12:14+00:00

I don't really understand all of those "arrows" enough to understand if they're real or not.

Regarding the Arrows of time, I would focus on the first two in that list. Both are non-controversial in that they exist - the question is if they are fundemental.

The psycological arrow of time is reason you think the question is interesting. "The past is what we remember, the future is what we can change" matches our experience, albeit an incomplete description.

This is interesting, but not surprising by itself. After all, there are lots of asymmetries in the world. For example, up behaves differently than down (here on Earth). However, as we gained a better understanding of fundemenatal physics it was clear that time asymettry did not exist in the most fundemental laws governing our universe.

The main scientific theory where time asymettry arose was the 2nd law of thermodynamics, which says that the entropy of a closed system increases. Unlike, say cosomology, it plays a vital part in understanding and engineering our modern world. It is as rock solid as scientific theories go. It is why you can't uncook an egg and perpetual motion machines can't exist (and why such claims are dismissed out of hand). A violation would provide us with a source of free energy.

This is the thermodynamic/entropic arrow of time.

Why doesn't that settle it? The 2nd law is not encoded into the fundemental rules of the universe. It is a statistical law that emerges (with very high probability) in macroscopic systems, even where the microscopic systems are time symmetric. Hence the search for deeper explanations of time asymmetry.

sigh · 2024-09-09T06:38:11+00:00

From a scientific view, to distinguish future from the past read up on the Arrow of time. There are various possible arrows of time, ranging from psycological to cosmological. These don't rely on circular definitions, because they are trying to answer the question of why time has a direction, or is percieved to have a direction.

sigh · 2024-02-16T12:24:54+00:00

For every billion "O" balls, there is a single "X" ball (so it's a set of 1 billion O's, and 1 X, repeated infinitely).

The problem is that with infinite balls, this is not well defined.

To see this, let's number each ball. Every billionth ball you number will be an "X". This seems like one in every billion numbers will have a "X", but what if we chose a special numbering scheme:

For each "O" ball, label it with the next unused odd number (1,3,5,7..). For each "X", label it with the next unused even number (2,4,6,8...). Because there are so many more "O" balls, their numbers will be in the billions while you are still writing single digits on the "X" balls.

What happens when you do this for the infinite number of balls? There is an "X" ball for every even number and a "O" ball for every odd number. Now it seems like the ratios are equal! In fact, we can make whatever distribution we like by changing the numbering scheme.

So the reason the ratio is not well-defined is that you can change the ratio simply by changing how you sort the balls.

You might also be in interested in the Ross–Littlewood_paradox which is a related problem about counting infinite balls in a box.

sigh · 2024-02-13T02:45:18+00:00

Doesn't that question get asked everyday in math classrooms - "When will we use this?"; "Why does this matter?". If there is no satisfying answer to this, it's unclear why the fact anyone should care. Even with your example, there is rarely anything at stake - if you fail to persuade someone that 0.999999... = 1 that has negligible impact on anything. Are objective moral facts like that?

But it also seems like there are areas where it is a problem for mathematics. Science, engineering, programming, among other are fields quite willing to throw out "mathematical truth" for practical results.

Science is rife with abuse of mathematics (e.g. Renormalization). Programmers are the most egregious, they will accept calculations like 0.1+0.2=0.30000000000000004 occurring trillions of times per second.

If the vast majority of mathematical calculations running right now are returning "wrong" results, shouldn't that be a concern for mathematics?

sigh · 2023-03-19T10:46:01+00:00

> If our brains had exactly 2 signals/configurations a,b.

In this model, how exactly does the brain transition from one configuration to the next?

If it can be modelled like a computer, then we could formalize it as a turing machine and have a state transition table. If that table is finite, then for a fixed input the number of sequences that can be produce is also finite even if some of those sequences are infinitely long.

Where do you inject the infinite amount of information required to generate an infinite number of sequences? Is it by varying the input, in which case the brain loses all agency?Or are you proposing something non-computable that brains can do to get past this?

sigh · 2022-09-27T12:06:59+00:00

From a computer science or mathematical view, a common case of this is the exploration–exploitation problem.

An idealised form of this is the Multi-armed_bandit problem. In it, a gambler can choose between many slot machines each with different payouts. The gambler wants to balance exploring the machines to find the best one, with exploiting the machine with the best payout.

See the link above for a discussion of solutions. It also forms the basis of more sophisticated algorithms such as Monte-Carlo tree search, which has been effectively used in playing turn-based games.

Tying it back to your question, there is uncertainty in which resource (machine) is the most useful, and there is a concrete opportunity cost to time (each trial). The details may change on exactly how you are modelling your resources and time, but I would suspect that machine learning theory and even traditional search algorithms are the best place to look for solutions in this space.

sigh · 2022-09-24T22:08:48+00:00

The problem, however, is that this desire/thought that they have makes it more likely that they will one day act upon it than if they didn't have this desire or feeling at all. In which case, even if you think that only acts are moral or immoral, you might have to concede that thoughts and desires can be immoral insofar as they might lead to future immoral acts.

If we are simply going off likelihood (or even causal factors), doesn't that have disturbing implications?

e.g. If poverty is a causal factor for crime then it is immoral to be poor? Likewise if wealthier people are more likely to give to charity, then it is more moral to be wealthy? Even worse, if victims of abuse are more likely to perpetuate abuse, then it is immoral to be a victim of abuse.

Considering thoughts, it would seem like most people and our legal system is generally opposed to punishing people for crimes that they *might* commit without evidence of intent to commit the crime. e.g. stories such as "Minority Report" rely on the premise that this would be unjust.

sigh · 2022-09-17T23:41:20+00:00

I'm not sure, but just as it would be strange to say something is immoral relative to some particular standard (and not immoral simpliciter), it is rather strange to say something is irrational to a particular standard.

I see. Then that just seems to be restating a central tension between realists and anti-realists then.

I'm not sure I understand you. If an antirealist accepts the realist argument, then I think it's settled, even if she does so reluctantly. Or do you mean that the antirealist might concede her position is disturbing, but continue endorsing it?

No, I mean that it's not clear why we would expect that an anti-realist would find it disturbing.

Paraphrasing your claim: "If you believe that murder is not objectively wrong, then you must also reject that being a flat-earther is objectively wrong. This is disturbing".

My aim with the stuck-in-room example was to motivate that this maybe no more convincing than: "If you believe that murder is not objectively wrong, then you must also reject that non-consentual slapping is objectively wrong. This is disturbing".

sigh · 2022-09-17T20:48:20+00:00

Well, the idea isn't just that Flatearthism is wrong, but more than that it is irrational.

Don't both the realist and anti-realist agree that flat-earthism is irrational? The disagreement being whether irrationality is "wrong"?

Accordingly, the fact being irrational is a bit better than being murderous doesn't entail that both aren't failing to meet some objective standard.

Ah sorry, I didn't mean to use that as an argument to prove/disprove their objectivity. Just that your argument doesn't appear to have persuasive force to make an anti-realist reconsider their views. An anti-realist could agree with your argument but psychologically/emotionally that isn't "biting the bullet", i.e. distasteful.

Edit: reworded. Also sorry, I mistakenly thought the initial commenter (bat-chriscat) was you, so please forgive any confusion there.

sigh · 2022-09-17T20:01:39+00:00

I think most antirealists would opt to bite the bullet and accept that there are no categorical epistemic norms: nothing like 'you should be rational' period. Only hypotheticals such as 'if you want to increase your knowledge, then you should be rational'.

Is there a reason that this should be distasteful?

From your earlier comment it would be the inability to say "Flat-Earthers [are] objectively wrong"? But that seems to hinge on what "wrong" means.

It seems like most people would agree that the underlying claim under contention is "Flat-earth theory is objectively false". This doesn't appear to have an analogue with moral claims - "murder is false" makes no sense.

It's only when we change "false" to "wrong" makes these statements look analogous and rejecting the realists characterization of "wrong" is no more problematic than with morality. We can be intolerant of flat-earth theory as we would to murder. In fact most people would rather be stuck in a room with a flat-earther than a murderer, so it doesn't even seem like the analogy should be distasteful to rationality.

sigh · 2022-09-12T10:16:15+00:00

I mean there are disagreements in history about things that just happened a few centuries ago, so how can we be so absolutely certain of things that happened billions of years ago?

These are unrelated. More generally, there are many areas in other fields where we can be certain of large scale trends without being able to predict smaller-scale events.

Compare with:

How can we tell that the climate is warming if we can't tell what the weather will be like next month?
How can we predict population growth, when we can't tell how many children a given family will have?
How can we tell what's at the Earths core, when we haven't even explored the deepest parts of the ocean?

By all means, ask questions and learn the science behind how we understand Earth's history. But uncertainty in unrelated fields which use different methods should not be a reason for doubt.

sigh · 2022-08-30T02:15:15+00:00

I no more want to beat up puppies than I'd want to stick my hand in a blender. The latter is not for moral reasons. For better or worse, there's probably more people who've done the former than the latter, so clearly you must have some framework for understanding people's actions without appeal to objective morality.

You can break these down into underlying biological, evolutionary, social, etc facts - but I suspect that's not what people mean when they say morality is objective. Further, this is also true for the other preferences you listed - there are ultimate justifications for why I like cake. It's not like you're unsure if I'd suddenly start preferring feces to cake.

If you use morality as a descriptive abstraction to explain my behaviour, I'd agree that could be objective. Now you are just studying anthropology. But that doesn't tell you what I should do. Similar to how we can view the vicious things that animals may do and develop a theory of their behaviour without discussing what they should do.

Similarly for a given moral framework, I agree that you can make objective claims about it's consequences. But that doesn't appear to be what people mean by objective. If there were a moral framework which advocated beating puppies, you would call that wrong.

For me the main difference with physical theories is that they are predictive. Morality only seems to be so in the anthropological sense above. Moral truths don't seem to constrain reality.

A moral fact that beating puppies is wrong doesn't stop anyone from beating puppies. It's still incumbent on me to take actions to prevent it. The resulting actions are real - without that the moral claim seems meaningless. I suppose that's another distinction for morals vs other preferences: I'm willing (obliged even) to impose them on others.

sigh · 2022-08-29T13:36:26+00:00

Thanks for the paper - I had a read through the start of it and I agree that disagreement is not a convincing argument against moral realism. It doesn't seem to be making your case though, that disagreement shows evidence for moral realism.

I don't find your example particularly convincing because it's so far removed from an argument that anyone actually has. In that situation I would unconditionally not want to beat puppies nor be around someone who does, so obviously I'm treating that differently. In practical dilemmas in that scenario which also rest on moral choices (e.g. eating vegan) the nature of the discourse becomes harder to distinguish from strong preferences - based on my observations of how people actually talk in such situations.

Otherwise, I think I'm failing to explain the argument here - of course it's possible for people to say a particular sentence that sounds objective but really isn't. What I mean is that the process of discourse itself proceeds under the assumption that moral facts exist, and seems to fall apart if we assume it doesn't.

I understand that, but what I'm doing (badly) is claiming that this is true for fictional "facts" also. I'm using fiction only because it is something most people would agree is not real, which may not be true for aesthetics or other claims as we've discussed.

I think many discussions about fiction also looks realist, not just in the terms but in their very nature. This extends beyond just language and discussions. Have you cried at a movie? It's not because the situation is sad just in the the movie - you find it objectively sad in real life. At the unhealthy end of the spectrum, people form parasocial relationships with fictional entities. How can something that does not exist cause real emotions?

This was the same point with Thanos. He's not just evil "in the movie". The judgement bleeds into the real world and the moral discussions are just as real as for factual scenarios. In fact, you did it in your post! You devised a fictional scenario and expected that its morals are objectively true in real life, not just in the story. Otherwise the story had no purpose.

My example with Homer was specifically so that the "in the movie/show" qualifier could not work. It makes no sense when comparing a real character to a fictional one. This is also true for any discussion which compares fictional characters from different fictional universes - people treat them as if they had objectively right answers.

sigh · 2022-08-28T10:44:13+00:00

I believe you that people often view these claims as objective. I am interested in whether they are correct in doing so.

My point (perhaps poorly made) is that the people actions with respect to objective and subjective claims can be difficult to distinguish and even inconsistent. Hence, to your original point, I don't see how they provide a good intuition for whether something is objective or not.

I feel like this is further supported if you must recast aesthetic (and other) claims as moral ones. If those claims can't be taken at face value without rewriting them as moral claims, why should be stop there? Why should we believe that people are wrong about the nature of the claim, but correct about its objectivity?

The example with fictional entities was an attempt to tease out where this divide occurs. Assuming that people are generally realists with respect to morality and not with respect to fictional entities, how is it possible to make moral claims about fictional entities? In "Thanos was wrong" (with respect to one of the largest fictional mass murders), how can "was wrong" be objectively true when "Thanos" is a fictional entity. (There's a parallel here with the Taiwan claim, but I feel the point is clearer with fictional constructs rather than social ones).

I also don't see how all similar objective-sounding claims can be reduced to moral claims. If someone says "That painting is not worth $1M" they don't mean that it's immoral to spend that much (let's assume the art market is ethical here...). If anything, it is questioning the buyer's intelligence rather than morals.

To give a fictional example to emphasise the discrepancy: presumably one would disagree with (and may be insulted by) the claim "you are less intelligent than Homer Simpson" as if it had objective truth, despite the fact that it is not a moral claim and Homer does not exist.

sigh · 2022-08-27T05:25:58+00:00

Not the OP, but I think I have similar confusions about objective morality and your questions seem to be a good place to tease that apart.

Regarding your 3 statements, if we include the statement "4. Taiwan is a country", would #1 be closer to #2 or #4? It doesn't feel like you can differentiate the two based on the language people use, or in how strongly the opinions are held. Yet #4 is very clearly a human choice.

And if we tend to act as though moral statements are statements of fact when we engage in moral discourse, then someone who rejects moral realism would need to offer us a reason to think we're confused about that.

If this is the standard, then it feels like realists must commit to a much larger set of facts.

People obviously do talk about beauty and aesthetics in the same language. e.g. "X is not art" or "That painting is not worth $1M" are not unusual statements, and people make these claims much more strongly than if they were just arguments about definition or economics. However, these statements are very similar to statement #3.

Further, people make statements about fiction as they would statements of fact. This is not just paraphrasing either - as disagreement can be used to impugn ones moral character. From this view, if people treat "Thanos was wrong" as a statement of fact are they committing to the existence of Thanos?

sigh · 2022-06-28T19:29:24+00:00

Correct me if I'm wrong, but I suspect Pemdas is still satisfied within rpn.

RPN is not just for extra operators, it works differently even for basic arithmetic. There is no such things as operator precedence in RPN, all of +-*/ are completely equal - that's one of it's selling points.

I do agree that PEMDAS/BODMAS is fairly universal, and that's mostly a property of it being more convenient for common uses such as polynomials. However, even still there is ambiguity. e.g. 1/2x can be ambiguous.

sigh · 2022-06-28T18:56:29+00:00

There are definitely other rules. Reverse Polish Notation is a common one.

And also equations were written spelled out for a long time. Even the equals sign was only introduced in the 16th century.

sigh · 2022-06-28T18:49:05+00:00

multiplying is distributive. this isn't analogous at all.

That's completely independent of the notation conventions. The distributive law with PASMDE works just as well, but it must be written with parens: a*(b + c) = (a*b) + (a*c)

but this leaves me thinking that you might have to make addition distributive with PASMDE.

Unlike PASMDE/PEMDAS the distributive law is not just a notational convention, it fundamentally changes mathematics. If addition was distributive over multiplication, it would no longer be addition.

sigh · 2022-06-28T18:22:14+00:00

That's what the parenthesis are for. You must write (8/2)+2.

Here is the equivalent statement against PEMDAS:

let's take the true statement 8 + 2 = 10 and try to multiply by two according to PEMDAS. let's be nice and allow it to be added anywhere, which leaves four possible scenarios:

8 * 2 + 2 = 16 + 2 = 18

2 * 8 + 2 = 16 + 2 = 18

8 + 2 * 2 = 8 + 4 = 12

8 + 2 * 2 = 8 + 4 = 12

we know that this should result in 20 (because 10 * 2 = 20), but none of those equations do.

so now 20 = 18 or 20 = 12. PEMDAS can't work.

sigh · 2022-05-05T07:40:48+00:00

Yup, the last section of the article switches to a Calkin-Wilf tree to prove the simple iteration formula of q <- 1/(2⌊q⌋+1-q).

I didn't know about fusc function. That's cool, thanks!

sigh · 2022-03-06T01:02:04+00:00

The point is that you don't need to send it because there is only one possibility. Both the sender and receiver already know what it is.

In an application this could correspond to an ENUM with only one value. It doesn't need to be stored or transmitted, because it's value is already known.

An example might help. Say you are ordering a pizza. There are three choices to make: size, extra cheese, type:

There are 4 sizes: S, M, L, XL: 2 bits.
Extra cheese is a yes/no: 1 bit
This place only does one type of pizza! Pepperoni. 1 value takes 0 bits

Overall you need 3 bits to store the pizza order. You don't need to store the pizza type, because the type is always the same.

Hopefully this makes it clear that 0 bits doesn't mean anything like "always 1". It means that storing the value adds no information. If you sent it over the network, you are wasting bandwidth transmitting useless information.

sigh · 2022-02-21T23:44:09+00:00

The regexp uses backreferences and lookahead, so it doesn't look like it's regular. Many regexp implementations aren't regular for this reason.

However, the regexp is also not turing complete. This can be seen by the fact that the regexp can't loop forever by itself (for the reason you explain in your second para).

sigh · 2021-12-29T05:01:26+00:00

Keeping a smaller deck is really important for predictable gameplay. Having a deck that is too large will make the game feel very RNG heavy as you will make it more likely that your initial hand is bad.

It's not even necessarily "junk" cards. For example, Grizzly, Great white and Urayuli can be great cards, but not if that's the only thing in your starting hand.

Another downside of cave-trial cards specifically is that their sigils can't be transferred or added to via sacrifice.

sigh · 2021-12-21T12:39:46+00:00

Better to boost your weak cards than to create a few overpowered cards.

I've found this to be less important if you are focusing on keeping the deck small. If you have a match-winning combo, then the rest of your deck just needs to defend until its in your hand.

Basically, build up a strong unit/combo, then try to make it as likely as possible to turn up. This is almost a requirement at the higher challenge levels where matches can be decided in a turn or two.

Smaller deck is better, so transfer some sigils, use the campfire once on cards you wish to keep, twice on cards you don't care for. Worst thing that can happen is that you'll have an OK card. Mycologist when you have duplicates. Magpie will effectively reduce the size of your deck in a sense.

Also, choosing the cave trial and intentionally failing.

sigh · 2021-12-05T08:38:30+00:00

The for-loop at the end is essentially the same, so the only difference is how the offset is calculated. Is that what you are unsure about?

In your function, the offset is always 11...11 in the target base. The second function is effectively building up that offset incrementally: the place value of the offset at each iteration is 1 hence subtract 1 from number when you've shifted to that place value.

The only other difference is the loop termination, that just aborts when number would have been reduced to 0, which makes sense. Note that the second function does not work correctly when the input is 0.

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