Aleph was once more sitting in for ‘class’ Elsie was an interesting instructor. In contrast to Omega’s methods which were often on the lighter side of traumatizing to make sure that Aleph was most competent and retaining the information of her training the Alien seemed to be favoring a much slower and more scattered approach to teaching the Terrans.

There had not been any drills in airtight bags filled with stinging bugs yet!

"The plan for this lesson was to continue the previously interrupted one. To review working to improve your abilities of spatial and temporal bearing.”

The screen momentarily flickered through the previous lesson’s timeline in a flickering rapidity that gave Aleph pause. Hadn't Squidgie already talked with them about not presenting things so quickly?

“However it has been correctly pointed out by Von Squidgeworth the First Esquire that this was premature and you lack some prerequisites, so further developing these will instead be the focus. These are primarily numeracy, sense of scale, and conceptual tools to apply these and avoid scope insensitivity."

The screen blanked to a soft white, then a single black dot.

“Numeracy is the capacity to read, comprehend and convey quantities and numbers in a useful scope for interconnected polity life.”

The number one faded into being in clear black above the dot and a soft voice spoke the word ‘one’ under Elsie’s lecturing tone.

“Terran civilization as with most recent uplifts has what most polity would consider inadequate numeracy. Your specialists have created jargon and mechanisms of approximation that approach the necessary skills and within your own habitat and niche this limitation will not come up.”

The dots began splitting, the number changing the two, the voice speaking softly the same. Then four, then eight.

“However it does not change that as a population your general capacity for comprehending, conveying and utilizing large numbers is stalled and stunted. Even amongst your experts there are tendencies which linger and become apparent even with comparatively insignificant quantities.”

‘Two-Hundred and Fifty-Six’ chimed out in the opening that Elsie left for it.

“Consider this one. In most polity exchanges and especially in dealing with Inter-polity trade this is an utterly insignificant quantity. There are many orders of magnitude more ATOMS then this number in even the smallest cell of your body. And yet your linguistic and thus associative cognitive apparatus already begin to strain and stumble at even this minute and tiny amount”

Aleph tilted her head and glanced at Omega and then Quarti.

“Why would we need to count things in atoms though? Why not in something larger? Like the cells, or maybe ya know, whole people?”

Elsie shifted its arrangement of cubes and boxes. Unlatching connecting arms and withdrawing them until there were two distinct columns of it standing there. One with a screen and another with an approximate assemblage of the same shape.

The last tube retracted from between them but they continued to stand and survey the class of the Terrans and Squidgie.

A voice emerged from both sides.

“Am I one or Two? Am I whole or separate? On what basis can you define one assemblage of atoms from another?”

The tubing extended back and the two distinct assemblages joined and reshuffled until they were a single lounging assortment.

“The reef and the polity within it have a far wider spread of perspectives and intuitions then between us. This fundamentally changes what border and category criteria are needed for individual objects. To facilitate trade and interaction the polity as a whole have had to find common measures. Ultimately there has emerged only one true collection of sufficiently common and universal measures and all polity, culture and language adhere and adapt to utilize it.”

The dots began to split again, the voice whispering feverishly fast to keep up the number above the space that now looked more like a grey shimmer then individual dots ballooning madly.

Omega was tentative, her voice strained as if she was expecting a rebuke which honestly made Aleph wince. Pylo had hurt her friend and mentor’s confidence in a way that she had never expected to see. But then again she could see how it would make her stronger.

Eventually.

“That’s what we have the scholars notation for though, to deal with large numbers like this.”

Elsie nodded and above the larger number a much smaller and simpler set of symbols appeared.

The voice spoke softly in a clear chime, different and distinct. The numbers pulsing blue as it spoke.

First all at once.

“Two to the Thirtieth”

Then holding in odd chunks as it slowly worked through the numerals.

“One-Billion Seventy-Three-Million Seven-Hundred-Forty-One-Thousand Eight-Hundred And Twenty-Four”

Finally flashing in sharp distinct triplets and then individual numerals.

“gun lʌni thʌnænu doʊnenæ”

Aleph tilted her head to the side a bit. It sounded somewhat foreign, but the consonants and vowels were not impossible to parse. It mostly just seemed like slightly musical gibberish.

“But tunie does not even use SOUND for her language, that can’t be all that universal.”

Elsie bobbed their screen and spoke gently.

“That is so, however a readily determinable mapping of distinctly recognizable phonemes have been found for your physiology and sensory systems. This has been so within every language and sensoria that is used by species capable of contributing to inter-polity affairs. It is recommended that you either utilize the template I’ve found in the archives for previous Terran polity, or develop your own with similar capabilities of compression and utility”

Omega leaned forward with one of her more intense looks.

“That has the tone of something a lot more like a warning or a threat then these usually go. What would it mean if we don’t?”

Elsie tilted their screen down in something that vaguely could map to solemn.

“Only those species deemed incapable of having the necessary scope of abstract thought for interpolity affairs have ever failed to have sufficiently distinct identifiable linguistic signals to properly map this standard to their own language modalities. If your own polity fails to reliably show signs of at least this basic numeracy your population will eventually not be considered capable of self governance and be categorized by your neighbors as either domestic chattel or feral unclaimed resources.”

Omega’s expression went hard, Quarti matching her with a thin lipped frown.

Aleph felt her tongue starting to go a bit dry and snapped her jaw shut to swallow hard.

“The fate of either in the reef is to be protected, modified, preserved, exploited, ignored or cleared as the more relevant polities and their citizens see fit. Your species deserve better than that. You are capable of more than that.”

Omega stared at the screen and its collection of numbers.

“Why can’t we use the scholar’s notation? We all know it. It would suffice to show we are competent right?”

The numbers changed subtly, although the grey not quite shimmer mist below them that presumably were the dots did not noticeably shift.

“Two to the Thirtieth Minus One”

“One-Billion Seventy-Three-Million Seven-Hundred-Forty-One-Thousand Eight-Hundred And Twenty-Three”

“gun lʌni thʌnænu doʊneni”

Elsie turned their screen back to Aleph then Omega.

“It produces cumbersome extra verbal payload and approximate additions to your thinking. It does not readily leverage your highly verbal and linear thoughts as effectively. It becomes less succinctly compact and opens up more logical operations to contain the same information. This introduces less ability to utilize your intuitions, less ability to hold the reality of the numerical categories clearly distinct. More capacity to make mistakes.”

Elsie looks back at the screen and the numbers begin to shrink rapidly. Until once more a single dot and a single number showed.

The voice of before chimed again.

“One”

“Dun”

“In contrast this is a compact and definite numeracy method which should readily suit your sensory and memory adaptations well while not sacrificing clarity or specificity”

“Two”

“Den”

Squidgie perked up a bit with a waggling of a few arms and a tilted body. A manner that let them approximate the amount of attention that a human simply raising their hand might draw.

“Miss El-szie! This is very interesting but Is this really the least cumbersome way to assist the Terrans in Numeracy? In Redweed after hatching me and my clutch mates were shown how to speak MUCH more compactly. And all of this geometricizing of the concept just seems strange and over complicated. Why all the ratio referents?!”

Aleph blinked a little bit and looked back to Elsie

"The terrans don't have a quantitative cortex or analogues structure like we do, They would find tracking numerals by prime factors almost impossible. They will effectively have to emulate all of that memetically. This is not an uncommon limitation in more feral species, Hence the existence of the methodology"

Aleph blinked a few times then looked at Quarti and Omega and raised a brow, Omega leaned her head forward and flicked a slight ascent to her over the choir.

She spoke up to fill the space before the lecture continued.

“So you both have... uh... a brain lobe just for math? Like a calculator in your head?”

Elsie’s screen jolted with a rush of activity rates on various stocks and strategies. It was a torrent that only slowed after a few seconds. Finally voice was given to the internal traffic that Aleph’s question had precipitated.

“Technically I have several, But Von Squidgieworth the first Esquire does not beyond a more or less general optimization scheme of various sub anatomies. No This is purely a mechanism for appreciation of numerical qualities from sensoria. Actual computation and complex theory is still mostly manual for them as it is in most Animalia species.”

Aleph tilted her head. Wait Isn't dealing with and recognizing properties of numbers what Math was? She was going to have to ask Pylo to help with translation checking this session it seemed.

"They do however have *three* distinct modalities which together effectively reproduce those capabilities and far far more; the quantitative cortex, symbolic lobe, and histrogamic area.”

The view shifted to what she swore would be a PowerPoint slide, if you drew it up on a screen instead of singing it over the aether, showing the three areas and what functions each corresponded to.

“However at the same time Human anatomy is similarly divided into highly acute visual and geometric processing sections, linguistic and pattern recognition focused abstractions that have comparable if differently optimized focus towards your own ‘mathematics’ cortex. For Example, Catch."

Elsie tossed the book up in a simple arc and over to her.

“Can you explain how you just did that Aleph?”

She looked down at the book in her hands.

“I just saw you toss it and caught it? Uh... I put my hands where it was going to be?”

She looked around, Quarti was grinning and nodding, Omega seemed just as confused as Aleph. Von Squidgie was trembling with what she was pretty sure was excitement.

“You... You can just know where the arc goes?! Without doing any formulations? No Calculations?! That thing was *tumbling* and with *air resistance*, and... H-how... I have been deeply misrepresenting your equivalent Person scores! If you can do that then-”

Elsie interrupted with a harsh beeping tone.

“Our ship Mistress Pylo has already corrected me several times on my clumsy use of that term as presented. Furthermore Von Squidgieworth the First Esquire, you are not qualified to judge and nor have you performed anywhere near the rigor needed for a full evaluation of an individual organism’s rating for that score, you'd be much better off just doing a linear regression on neuron count. Also while associative tangents can within reason be beneficial to retention in terrans we are deviating from an important development of fundamental skills.”

The screen turned back to Aleph, Omega and Quarti.

“Now then for maximum associative linkages please observe, listen and repeat as we work through these patterns”

The Dots, Numbers and chiming soft voice returned.

“One, Dun”

Aleph glanced at Omega and then back at the screen with a bemused look.

“Two, Den”

Quarti seemed to be enjoying it at least though, but then again Aleph was pretty sure that the last time Quarti had been to a classroom beside’s Elsie’s was before the steam engine was invented.

“Three, Din”

Aleph sighed. She had not expected that she would be getting taught how to count by an alien. If calling Elsie "an" "alien" was even correct, or if they were more a swarm of robots, or a miniature city, or-

“Four, Dæn”

Whatever.

“Five, Dɛn”

This was just not what she expected learning the ancient technology and secrets of interstellar civilization would entail.

“Six, Dɪn”