In geometry, as laid out by Euclid [1] in around 300 BC, it is postulated thatwe can:1.draw a straight line from any point to any point,2.produce a finite straight line continuously in a straight line,3.describe a circle with any center and distance (radius),4.understand that all right angles are equal to one another,5.and finally, understand that if a straight line falling on two straight linesmakes the interior angles on the same side less than two right angles, the twostraight lines, if produced indefinitely, meet on that side on which the anglesare less than two right angles.For our purposes, this can be simplified to1.…. . …….. …. …. … ….. .. … …..,2.……. . …… …….. …. …….. …. .. . …….. ….,3.…….. . …… …. … …… … …….. (……),4.………. …. … ….. …… … ….. .. … …….,5.… ……., ………. …. .. . …….. …. ……. .. … …….. ….. …. … …….. …… .. … …. …. …. ….… ….. ……, … … …… .. ….., .. …….. …………, …. .. …. …. .. ….. … …… … …. …. …….. …….We see clearly that the fifth postulate stands out. It is longer (comparable to thesum of the length of the initial four). It too seems less fundamental and moreconvoluted. And yet our intuitions tell us it is a property of geometric spaces—might it then not follow from the initial four? From the birth of Euclideangeometry up until the late 18th century, three things were true:1.Mathematicians broadly thought the postulate a necessary feature of geometry.2.Mathematicians broadly thought the postulate could be derived from the firstfour.3.Mathematicians were unable to derive it from the first four.fifth shows the fifth postulate visually: if two lines are not parallel, they willeventually cross exactly once; in our case a few centimeters to the right of wherethe figure ends.Only in 1872 was the problem finally resolved by the Erlangen program [2].The fifth postulate, rather than being a true property of geometry that we wereso far unable to prove, was but a postulate of a particular kind of geometry,now known as Euclidean geometry. Geometry, however, is much broader thanthat. The Erlangen program paved the way for non-Euclidean geometry, famousexamples of which are hyperbolic geometry and elliptic geometry, both of whichfollow from varying the fifth postulate, and are in broad use today, a prerequisitefor much of physics, engineering, math, etc. Non-Euclidean geometries surroundus: we live on a sphere, many conceptual spaces seem to bend in all kinds ofstrange ways. Indeed, M. M. Bronstein, J. Bruna, T. Cohen, and P. Velǐcković [3]introduces geometry deep learning. So why the multi-millennia-long confusion?It has been argued [4] that the use of the terms “line” and “point” in Euclid’spostulates were so pregnant with association from our real-world experience,that we implicitly, without knowing so, attributed qualities to these mathematical constructs. If using the terms “line” and “point” will lead humanity on atwo-millennia-long treasure hunt, what might terms like “artificial intelligence”,“neural network”, and “evolutionary computation” do to our clarity of thought?These terms are obviously sexy to say. The terms are sure to have playedessential roles in fundraising, product pitching, PhD applications, and even theoccasional one-night stand. But alas if the price of unnoted confusion is a halt toprogress, something must be done. Clarity of thought is a core value of the VirianProject, and thus, it is in this spirit that we produce the dictionary for clarity ofthought seen in Table 1. If nukes, as some have said, are viagra for politicians[5], so too the use of these overly smart sounding terms is for the scientist. You,dear reader to the extent that the profession applies, are encouraged to use theseterms in academic writing, but fear not, for one-night stands and fundraising,pop a pill, and go from the 2nd to 1st column.Viagra termVirian termneural networklayered filterdeep learninglayered filteringlanguage modeltext modelfoundation modelmodality modelevolutionary computationgenetic programmingartificial intelligencemachine learningReferences[1]Euclides, T. L. Heath, D. Densmore, and Euclides, Euclid's Elements: AllThirteen Books Complete in One Volume. Santa Fe, NM: Green Lion Press,2007.[2]F. Klein, Elementary Mathematics from an Advanced Standpoint. Geometry,Dover edition. Mineola, N.Y: Dover Publications, 2004.[3]M. M. Bronstein, J. Bruna, T. Cohen, and P. Velǐcković, “GeometricDeep Learning: Grids, Groups, Graphs, Geodesics, and Gauges,” no.arXiv:2104.13478. arXiv, May 2021. doi: 10.48550/arXiv.2104.13478.[4]D. R. Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, 20th-anniversary ed. London: Penguin, 2000.[5]A. Sirkis, Descarbonário. Ubook Editora, 2020.