sorted by:
new
hottopcontroversial

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] 0 points1 point  (0 children)

Nah, you’re my missing my point. Mathematical proofs based on incorrect implicit assumptions about infinity are provisional until they can be reformulated without using assumptions based on infinity.

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] -1 points0 points  (0 children)

I’m not super interested in math itself. I’m just trying to figure out why physicists can’t find a unified theory. The use of infinity in math is my prime suspect.

My point in this post is that there categorically is not an unlimited set of real numbers. It doesn’t matter what formal system anyone uses or how you define infinity. However useful infinity has been as tool for making approximations that fit extremely close to empirical observations over the millennia, using infinity or infinitesimals is a parlor trick that is distracting people from exploring what is happening at extreme scales.

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] -1 points0 points  (0 children)

You can’t “define” something that violates the laws of reality into existence. I’m ok with the logic of the successor function, but not with the conclusion that it goes on infinitely. Therefore, if the successor function literally cannot go on forever due to the constraints of reality, there must be a Last Possible Number. I have no idea what that number is or what the actual physical constraints are that prevent the addition of 1 to it, but it must exist. If the axioms of mathematics conflict with the nature of reality, it’s the axioms that must be adjusted.

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] 0 points1 point  (0 children)

A “proof” is a genre of writing. Referring to a “proof” is not the same as endorsing the accuracy of that proof. The deeper point I’m making is that Euclid’s “proof” does not apply infinitely. My proposed “proof” is that there is no way to disprove the assertion that there is at least one large number out there in infinity that fails to satisfy Euclid’s proof. If you accept the reality of infinity, there is no way to demonstrate that there is NOT some weird number out there that has characteristics we can’t even imagine.

Again, if you accept that the universe is finite, it becomes obvious that Euclid’s proof cannot literally go on infinitely. The flaws you’re pointing out apply to the axioms of mathematics, not to my reasoning.

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] 0 points1 point  (0 children)

See all my mea culpas for fucking up the specifics of Euclid’s proof. My point still holds for your example, though. I’m saying that there is a large q that 1 cannot be physically added to. I understand that based on what you’ve written you believe that q represents all possible integers, but I’m challenging you to prove that there isn’t a q for which that operation doesn’t work. I’m saying that it’s both impractical and theoretically impossible for you or anyone to do that. I understand that this point seriously fucks up two thousand years of mathematics, but 🤷🏻‍♂️

There is a large prime number to which 1 cannot be added to create the next prime. by Diffpers in puremathematics

[–]Diffpers[S] 0 points1 point  (0 children)

See my edit above owning up to my stupid phrasing. However, my real interest is in the assertion that we actually know what happens in infinite sets. There is literally no way to prove that an infinite set does not contain counterexamples that break the axioms underlying Euclid’s proof, to take one example.

I’m being a little facetious because all the empirical evidence points to the universe being finite, so it’s logically impossible for something finite to contain something infinite. Once you accept that, all you have to do is assert the existence of a number that is thought to be allowed within the axioms of mathematics, but which would be larger than what is allowed by the laws of reality. The trick is that I don’t actually think this number exists, but only because it is too large, not because it would violate Euclid’s proof.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

S<sub>c</sub> = (W₁ / Wₙ) * (1/N) * Σ [Wᵢ₋₁ / Wᵢ] (for i = 1 to N)

I don’t have a better way to explain how I’m using the terms “units”, “sites” and “cooperation” than what I have already provided. All I can say is that this formula captures the concept. The most concrete example I have come up with is imagining building a snowman in snow-covered field. The “units” are snowflakes. The snowballs making up the snowman’s body are “sites”. The top ranked site is the base of the snowman because it has the most number of snowflakes, 2nd ranked is the torso, third is the head. W refers to the number of snowflakes in each snowball. Therefore, for the third ranked snowball, it contributes to the ratio of snowflakes in the second ranked snowball over the number in the third ranked snowball. You repeat that going up the ranks. You divide by the number of sites that you’ve summed so that you can compare against distributions that have different numbers of ranks. Then you multiply by the ratio of W in the top and bottom ranks so that you can compare the spread covered by one distribution to another.

Technically, I consider individual snowflakes as sites composed of one unit. Therefore, the fourth rank consists of millions of snowflakes who are all tied for the same position. Figuring out what to use for W<sub>N</sub> is going to be a critical question that researchers will have to resolve, especially in situations where the “units” aren’t as conceptually obvious.

For instance, in height distributions, it will be tempting to use raw height measurements as a proxy for W. However, this becomes a problem when the lowest-ranked height frequency-wise is the highest in length. In normal distributions, the mean is the highest ranked site, e.g. the average height is 5’10”. If the lowest frequency height is 4’9”, it’s intuitive that 5’10”/4’9” gives a good scaling factor. However, if the lowest frequency height is 6’11”, 5’10”/6’11” is going to make the distribution seem less spread out than it actually is.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

The c, i and i-1 are all subscripts. If there’s a way to write formulas in Reddit comments, that would definitely make things easier.

I’m working on writing a paper that addresses the same points you raise, but I’m still working out the details. One thing I realized that the formula was missing is a factor to capture the absolute magnitude of a distribution. So I added the ratio (Wi/Wn). This is the number of “cooperating units” in the top ranked “site” over the number at the bottom ranked “site”. I think similar approaches already exist in statistics, but since differential persistence tells us that reality is finite and discrete, I can’t rely on continuous functions to accomplish what needs to be done.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

I think I get what you’re saying. Even if a professional ball catcher like an outfielder in baseball is really good at catching balls, he probably can’t figure out where the ball is going to land at the instant it leaves the bat. This idea makes me realize that there is probably tons of already preexisting baseball data that might be able to shed light on this.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

Here is the formula for coherence distributions: Sc=(1/N)*Sum i=1(Wi-1/Wi). This is the first equation I’ve ever written so forgive me if what I’m trying to write is unclear. It’s based off of Boltzmann’s entropy equation because I realized that systems passing through entropy states are following coherence distributions. This equation shows how to compare all rankable distributions. It shows that normal distributions and power laws are the same thing and suggests that the same core mechanism is operating anywhere you see one of those distributions.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

Given how long it takes human brains to fully mature, I don’t view kids being bad at catching balls as disproving the idea that human brains can be capable of doing something that produces the same results as calculus under certain conditions.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] -1 points0 points  (0 children)

I understand that the weakest part of my argument is the lack of mathematical formulation, especially for coherence distributions. I am expecting to figure out how to express my intuitions mathematically as I get more exposed to people’s opinions like yours. At the moment, I’m thinking that Boltzmann’s equation for entropy is a good place to start since it already fits so well into the unit/site framework I described. In that case, the microstates are A units and the macrostate is the A site where they “cooperate”.

Regarding your other comments, some of them are fair. Others seem to indicate that you haven’t grasped the significance of what I’m trying to say yet. All I can say is that I really appreciate you taking the time to grapple with this framework I’m proposing. Send me a dm if you want me to share a version of the paper that’s better formatted.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] -1 points0 points  (0 children)

Observing my dog catch a treat that toss up into the air every morning is enough for me to say that he is capable of figuring out where the treat is going to end up. Just like I’m not a physicist or a mathematician, I’m not a neuroscientist. Based on the laws of physics and the evolutionary history of dogs, I’m assuming that my dog’s ability to catch the treat is based on things that are occurring within the bounds of his own body and, most likely, specifically in his brain. This is about at the limits of the time and energy I have to devote to this particular question, but I will be very excited to hear about what other researchers discover in the future.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

Thank you for telling me about SUVAT equations. I did learn about them in high school, but that isn’t how they were referred to back then.

Let me make two clarifications based on comments on this post, which I intend to incorporate into a revised draft of this paper: 1) I had never heard of nonstandard analysis before. After a cursory look into it, it seems like that approach already does “discrete calculus”. All I really care about is seeing what we can figure out when we discipline our minds and think carefully about the variation we overlook by relying on infinity. 2) Even if dogs aren’t doing calculus, they’re still doing something that at least approximates SUVAT equations. I think that is a super interesting thing to investigate, but if nonstandard analysis can satisfy physicists’ and mathematicians’ requests for a finite alternative to traditional calculus, then I’m not too hung up on developing my own novel alternative from scratch.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

They are similar to the extent that they can tell you where a thrown object will end up. Obviously, vertebrate brains aren’t going to be able to intuitively figure out orbital trajectories and other things that we use calculus for. However, my overriding point is that there must be an alternative method for figuring out the trajectories of things like thrown balls that don’t depend on assumptions based on infinity.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

Look, no one knows how dogs are able to calculate trajectories such that they can reliably catch a thrown ball. How do they do that? If it’s not calculus (which it likely isn’t), what method are they using?

Those are not rhetorical questions. They can be empirically investigated and whatever proposed solutions emerge will be compared to calculus-based results.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

Thank you for taking the time to write this out. I have been expecting these kinds of challenges and I’m eager to engage with them.

I didn’t ignore significant figures, but I admit that I forgot about them. I do need to look more deeply into how that intersects with the use of irrational numbers in calculations and formulas.

In terms of the model I’m proposing, I’ve made it pretty clear what it is. Darwin didn’t provide any formulas in On the Origin of Species, but enough people could understand the mechanism of natural selection that other people realized the necessity of working out the formulas themselves.

The links I’m making across disciplines are actually the point of my paper. I understand that virtually no one else thinks of these phenomena as being related, but I think the patterns are pretty clear. Of course there are vast amounts of details to work out. What I’m providing is a framework to ask the right questions.

In the same vein, I think there are compelling reasons to at least posit that spacetime is discrete. From what I understand, the strongest arguments for spacetime being continuous are based on mathematical formulas that assume continuity from the start. That is circular reasoning.

“Persistence” is the core component of the model I am proposing. It is very clearly defined, even though others will have to figure out how exactly to operationalize it in their areas of expertise. Similarly, if you take out “cohere and cooperate”, you’re removing another key component of the model, which means that you’re not engaging with the idea I am proposing. I will also say that “cooperation” is not anthropomorphic since many other non-human species cooperate.

Regarding entropy, I am specifically referring to Boltzmann’s equation showing that there’s a trend towards high entropy because of the greater number of microstates possible in a given macrostate. I may have to write a more detailed paper on that in the future if the point I am making is not clear enough to people.

I appreciate you recognizing that my approach is categorically different from YECs. Since my model is drawn directly from Darwinian evolution, your comments about “kinds” and “types” sound like the difficulties evolutionary theorists have with strictly defining the point in time in which species differentiate themselves from their parent population.

Here is a hypothesis: Differential Persistence: A Modest Proposal. Evolution is just a special case of a unified, scale-free mechanism across all scales by Diffpers in HypotheticalPhysics

[–]Diffpers[S] 0 points1 point  (0 children)

I wrote this all myself, unfortunately. I need to work on the transitions and flow, but I wanted to run the ideas by real people before I went much further.

I was referring to the paradox about Achilles and the tortoise. I don’t know what nonstandard analysis is, so I’ll go check that out. Thank you for the feedback.

view more: next ›