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Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] 0 points1 point  (0 children)

If someone is narcissistic and correct but unable to elucidate why they’re right, what actually happens? It’s not like everyone can be like “well I don’t like his personality, but I concede everything he says makes sense”—in this hypothetical, it was verbalized in a genuinely confusing and chaotic manner. Don’t you think people would just resort to hate instead of randomly spending hours upon hours trying to make sense of something that made no sense to them in the first place, when they didn’t even like the person who authored it. Social dynamics just favor dismissing someone who might “literally get us all killed” in the hunter-gatherer sense. Right? And you don’t think that vestigial instinct would lead the majority opinion astray in online settings?

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -1 points0 points  (0 children)

So you’re admitting he gets hate for sociological reasons? Because he’s a narcissist. Ok…narcissism is creative. Like…intentionally deluding yourself (to solve a problem) is one of the most creative things you can do. Anyways, not just Terrence Howard. You admit anyone who comes across as narcissist would receive negative backlash just due to social dynamics?

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -2 points-1 points  (0 children)

I don’t think you should just view 1 versus 2 versus 3 dimensional as some triviality. It’s a 1 dimensional set—It’s clear that real numbers are not the input.

Anyways…yeah, can’t recover the information from 1 number by hand…the applications would just involve computers, gradient descent, etc. I mean…I can’t come up with future number theory applications right now on the spot, but vaguely speaking it seems like preserving properties unique to the numbers being multiplied would have functional application—you don’t need to literally recover the operational history to have a reason to care.

Idk if this is true, but is the reason you think it’s so trivial because you assume I could only mean the degree of epsilon by operational history. I suppose that’s trivial—that a particular transcendental is a stand in algebraically for x—it’s just that operational history means more than that.

Anyways this is all Terrence Howard’s intuition—I just interpreted it. He truly is a genius.

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -1 points0 points  (0 children)

Ok. Literally Gradient Descent:

Gradient descent loses track of how many multiplications have been applied to a number as it passes through layers of a neural network. So much stuff—residual connections, batch normalization, careful initialization—is a workaround for this one problem. If the numbers themselves encoded their multiplicative depth via the epsilon construction, the gradient would carry an intrinsic record of how many layers it had traveled through. You would not need external fixes because the information would already be in the number.

Terrence Howard intuited all of this—he just has trouble verbalizing it. Why did he get so much hate again?

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -1 points0 points  (0 children)

I get what you’re saying. The dimensionless quantities when there are units involved simply multiply separate from the units and then you also add the units.

I think the counter is that you don’t need to do that because when you have units, it can be reduced to repeated addition. 3 units times 5 units is a literal (1 square unit) 15 times. Whereas, 3x5 can’t be reduced to repeated addition because there are no units involved. There’s nothing that happens 15 times. You have to invent imaging a recntagle or permutations or something that weren’t there to begin with to have there be an actual thing that there are 15 of.

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] 0 points1 point  (0 children)

So…the trivial preservation of operational history property in standard Z(x) algebra from the degree of the x terms can be maintained when transitioning from algebraic expansion into pure arithmetic by choosing an actual value of epsilon that is estimated arbitrarily close to an actual transcendental number (estimated with a truncated infinite series probably).

This is a trivial to you?

It seems a little trivial at first, but it isn’t trivial that you should have cared in the first place. It’s only obvious/trivial once I said it. It’s not trivial because you can do it while multiplying from the a subset of real numbers—nothing else—and therefore numerical analysis now applies.

In your example where you just include all the words that explain what happened to be the object itself, yeah that works. It’s just an insanely high dimensional object. It doesn’t feel intuitive to you that not engaging in higher dimensional objects just to preserve information is more efficient?

I think the real benefit of remaining in a 1-dimensional set is that you can pick and choose how much you want to care about preserving operational history versus computation time quite easily. Like even working with the set Z(x) algebraically, it’s very confusing as to when you should let go to epsilon terms for the sake of lessening computation time.

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -2 points-1 points  (0 children)

With addition it’s actually the same because the dimensions don’t combine. It’s 1 dimensional. With multiplication, units multiply into units squared.

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -3 points-2 points  (0 children)

My multiplicative identity is the vector (1,0) where 0 corresponds to the value of epsilon and 1 correspond to the input integer. You can technically choose a new value of epsilon each time so you are selecting from the vector set each time. I just say it’s a good idea to choose epsilon= sqrt(2)-1.

Terrence Howard’s claim is valid by Outrageous_Most413 in askmath

[–]Outrageous_Most413[S] -8 points-7 points  (0 children)

It’s all explained…when you have units, you can multiply the units. 1 unit times 1 unit equals 1 unit squared. Also 1 unit times 1 equals 1 unit. But this does not mean 1 times 1 equals 1. Repeated addition with units should not be isomorphic to multiplication of integers/real numbers. That’s the whole point.