Trying to understand influence peddling by looking at former Hawaii lawmakers J. Kalani English and Ty Cullen is like trying to understand astrophysics by studying the words to “Twinkle Twinkle Little Star.”

The three people involved deserve all the indignation we’re giving them. What they did was truly shameful.

But it is just a small part of a culture of political influence in which anything as crude and straightforward as bribery isn’t necessary because the influencers have other resources and other ways to get things done.

And the key to understanding the culture of political influence in Hawaii is not the bribe-payers but the big players who don’t need to bribe.

That kind of influencing is not a bribery problem. It may not even be against the law. But when people use the term “corruption,” they include this broader, vaguer notion because it seems sleazy and unfair.

And that’s OK.

For now, let’s call the person with this kind of access a “Big-Time Player.” And it’s an equality problem that goes beyond a few insiders who know how to do tit for tat.

A good way to understand this is to examine the political life of Milton Choy, the cesspool guy who paid off the two legislators, and compare him to Max Sword, the former lobbyist and police commissioner.

Choy is important because he is a very rare example of two sides of the influence coin. On the one hand — the hand everyone is stressing about — he blatantly and directly gave out money, hotel comps and — my personal totem of what it’s like in Hawaii — casino chips.

A direct, obvious quid pro quo exchange — the hallmark of a small-time political operator. That’s Choy the First, a small-timer.

In another way, though, Choy aspired to and for a time made the Big-Time Player list. He has given, depending on how you calculate it, between $160,000 and $300,000 in legitimate, publicly listed political contributions.

And he has spread this money around, much of it to legislators — as well as Gov. David Ige — many of whom have had no direct contact and who he probably never asked directly for favors.

That’s a typical way that large Hawaii donors like construction and engineering firms do it. No fuss, no grime. Good citizens spreading it around.

That’s Choy the Second. Choy the Small-Timer when he bribed, Choy the Big-Timer when he donated.

His small-time activities were blatant and illegal. His donor activities? That’s something more ambiguous, because Big-Time Player donations, of course, don’t come with any direct quid pro quo as in, “I give you campaign money and you then give me a lucrative contract.”

But when, say, construction companies donate to politicians, they aren’t exactly giving a generous gift as altruistic citizens, manifesting their patriotic largesse to fortify the democratic process that makes America great.

They do this to become members of an amorphous, informal but powerful mix of politicians, policymakers and some (really few) of the rest of us called the political class.

Like this: being connected; knowing what’s really going on; getting in touch with the right people; knowing how to develop a reputation as trustworthy, competent and discrete. Making yourself valuable if not indispensable. They become members of strategically important social networks.

And they often have lobbyists to help their cause.

Max Sword of Honolulu Police Commission fame is an example of a Big-Timer.

A recent Civil Beat profile described Sword as “a member of the political class’s inner circle” with “the resume to prove it.”

“For decades,” the profile continued, “when Hawaii governors, mayors and legislators needed to fill a seat on a powerful board or commission, they called Max Sword.”

Now, when Choy was behaving like a member of this political upper class and making all those campaign donations, he was awarded several lucrative government no-bid contracts.

There is no indication that he got them by bribing anyone. He did not have to because his campaign donations made him a presence, someone that important people heard of.

Not as well-known and indispensable as Sword, but at least a burgeoning member of the political class.

But then Choy went off the rails, behaved like a small-timer, ditched his subtlety credentials, bribed, and got nailed.

Lesson: Don’t be stupid, be subtle. Don’t be a caddy. Be a member.

And, as Edith Ann who is 5 1/2 years old would say, “that’s the truth.”

There are no easy legal remedies, partly because the activities are so hard to pin down, but also because much, probably most of what the Big-Time Players do is perfectly legal.

Bribery is easy to understand, and the remedies to deal with it are clear on the surface. English and Cullen took money. It’s obvious. Put them in jail. Pass harsher corruption laws. Strengthen codes of ethics for public officials, all essentially straightforward changes to the rules.

Will those things work? I have my doubts, but that’s for another time. Even if they are effective, though, they really apply to small-time corrupters and not the Players.

That’s because the problem of access, influence and the political class is more a political and economic issue. There are no easy legal remedies, partly because the activities are so hard to pin down, but also because much, probably most of what the Big-Time Players do is perfectly legal.

Access is a different kind of problem. When people complain about corruption, they often mean this kind of insider politics.

And they are onto something that shouldn’t be dismissed, because insider politics may be legal, but it’s also another manifestation of political and social inequality.

Studies have shown that politicians form their notions about public opinion based on the people who get access to them.

Take it down to another level and broaden the idea of who has access. Community meetings with government officials tend to be dominated by people who have more free time and more flexibility. Check out meetings involving housing and NIMBYs.

Some social networks offer support and information when it comes to getting access to a public official — as in, “Here’s who you should call.”

Other social networks lack this valuable information. For instance, people outside the loop have had a much harder time getting Covid-19 information and resources.

I guarantee you that my group of middle-class and wealthy friends are confident about whom to call when trouble arises. This knowledge, confidence and wherewithal is definitely not equally or even randomly distributed.

This may seem a long way from two legislators getting cesspool largesse. I am purposely casting a wide net here because the access and influence differences are part of this country’s birth-to-death inequality problem.

So, while you should be royally upset and angry about what some are calling Hawaii’s culture of corruption, keep in mind what that tells you about how things work.

But also keep in mind what it doesn’t tell you.